diff --git a/.github/workflows/docker-action.yml b/.github/workflows/docker-action.yml
new file mode 100644
index 0000000..0e6f1b6
--- /dev/null
+++ b/.github/workflows/docker-action.yml
@@ -0,0 +1,34 @@
+# This file was generated from `meta.yml`, please do not edit manually.
+# Follow the instructions on https://github.com/coq-community/templates to regenerate.
+name: Docker CI
+
+on:
+  push:
+    branches:
+      - master
+  pull_request:
+    branches:
+      - '**'
+
+jobs:
+  build:
+    # the OS must be GNU/Linux to be able to use the docker-coq-action
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        image:
+          - 'mathcomp/mathcomp:2.2.0-coq-8.18'
+          - 'mathcomp/mathcomp:2.2.0-coq-8.19'
+          - 'mathcomp/mathcomp:2.2.0-coq-8.20'
+      fail-fast: false
+    steps:
+      - uses: actions/checkout@v4
+      - uses: coq-community/docker-coq-action@v1
+        with:
+          opam_file: 'coq-mathcomp-cad.opam'
+          custom_image: ${{ matrix.image }}
+
+
+# See also:
+# https://github.com/coq-community/docker-coq-action#readme
+# https://github.com/erikmd/docker-coq-github-action-demo
diff --git a/.github/workflows/nix-action-8.18.yml b/.github/workflows/nix-action-8.18.yml
index 0f70c76..17eb4d6 100644
--- a/.github/workflows/nix-action-8.18.yml
+++ b/.github/workflows/nix-action-8.18.yml
@@ -4,30 +4,30 @@ jobs:
     runs-on: ubuntu-latest
     steps:
     - name: Determine which commit to initially checkout
-      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"target_commit=${{\
-        \ github.sha }}\" >> $GITHUB_ENV\nelse\n  echo \"target_commit=${{ github.event.pull_request.head.sha\
-        \ }}\" >> $GITHUB_ENV\nfi\n"
+      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"target_commit=${{
+        github.sha }}\" >> $GITHUB_ENV\nelse\n  echo \"target_commit=${{ github.event.pull_request.head.sha
+        }}\" >> $GITHUB_ENV\nfi\n"
     - name: Git checkout
       uses: actions/checkout@v4
       with:
         fetch-depth: 0
         ref: ${{ env.target_commit }}
     - name: Determine which commit to test
-      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"tested_commit=${{\
-        \ github.sha }}\" >> $GITHUB_ENV\nelse\n  merge_commit=$(git ls-remote ${{\
-        \ github.event.repository.html_url }} refs/pull/${{ github.event.number }}/merge\
-        \ | cut -f1)\n  mergeable=$(git merge --no-commit --no-ff ${{ github.event.pull_request.base.sha\
-        \ }} > /dev/null 2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n\
-        \  if [ -z \"$merge_commit\" -o \"x$mergeable\" != \"x0\" ]; then\n    echo\
-        \ \"tested_commit=${{ github.event.pull_request.head.sha }}\" >> $GITHUB_ENV\n\
-        \  else\n    echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n  fi\nfi\n"
+      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"tested_commit=${{
+        github.sha }}\" >> $GITHUB_ENV\nelse\n  merge_commit=$(git ls-remote ${{ github.event.repository.html_url
+        }} refs/pull/${{ github.event.number }}/merge | cut -f1)\n  mergeable=$(git
+        merge --no-commit --no-ff ${{ github.event.pull_request.base.sha }} > /dev/null
+        2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n  if [ -z \"$merge_commit\"\
+        \ -o \"x$mergeable\" != \"x0\" ]; then\n    echo \"tested_commit=${{ github.event.pull_request.head.sha
+        }}\" >> $GITHUB_ENV\n  else\n    echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n\
+        \  fi\nfi\n"
     - name: Git checkout
       uses: actions/checkout@v4
       with:
         fetch-depth: 0
         ref: ${{ env.tested_commit }}
     - name: Cachix install
-      uses: cachix/install-nix-action@v27
+      uses: cachix/install-nix-action@v30
       with:
         nix_path: nixpkgs=channel:nixpkgs-unstable
     - name: Cachix setup math-comp
@@ -38,8 +38,8 @@ jobs:
         name: math-comp
     - id: stepCheck
       name: Checking presence of CI target coq
-      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr\
-        \ bundle \"8.18\" --argstr job \"coq\" \\\n   --dry-run 2>&1 > /dev/null)\n\
+      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr
+        bundle \"8.18\" --argstr job \"coq\" \\\n   --dry-run 2>&1 > /dev/null)\n
         echo $nb_dry_run\necho status=$(echo $nb_dry_run | grep \"built:\" | sed \"\
         s/.*/built/\") >> $GITHUB_OUTPUT\n"
     - if: steps.stepCheck.outputs.status == 'built'
@@ -52,30 +52,30 @@ jobs:
     runs-on: ubuntu-latest
     steps:
     - name: Determine which commit to initially checkout
-      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"target_commit=${{\
-        \ github.sha }}\" >> $GITHUB_ENV\nelse\n  echo \"target_commit=${{ github.event.pull_request.head.sha\
-        \ }}\" >> $GITHUB_ENV\nfi\n"
+      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"target_commit=${{
+        github.sha }}\" >> $GITHUB_ENV\nelse\n  echo \"target_commit=${{ github.event.pull_request.head.sha
+        }}\" >> $GITHUB_ENV\nfi\n"
     - name: Git checkout
       uses: actions/checkout@v4
       with:
         fetch-depth: 0
         ref: ${{ env.target_commit }}
     - name: Determine which commit to test
-      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"tested_commit=${{\
-        \ github.sha }}\" >> $GITHUB_ENV\nelse\n  merge_commit=$(git ls-remote ${{\
-        \ github.event.repository.html_url }} refs/pull/${{ github.event.number }}/merge\
-        \ | cut -f1)\n  mergeable=$(git merge --no-commit --no-ff ${{ github.event.pull_request.base.sha\
-        \ }} > /dev/null 2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n\
-        \  if [ -z \"$merge_commit\" -o \"x$mergeable\" != \"x0\" ]; then\n    echo\
-        \ \"tested_commit=${{ github.event.pull_request.head.sha }}\" >> $GITHUB_ENV\n\
-        \  else\n    echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n  fi\nfi\n"
+      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"tested_commit=${{
+        github.sha }}\" >> $GITHUB_ENV\nelse\n  merge_commit=$(git ls-remote ${{ github.event.repository.html_url
+        }} refs/pull/${{ github.event.number }}/merge | cut -f1)\n  mergeable=$(git
+        merge --no-commit --no-ff ${{ github.event.pull_request.base.sha }} > /dev/null
+        2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n  if [ -z \"$merge_commit\"\
+        \ -o \"x$mergeable\" != \"x0\" ]; then\n    echo \"tested_commit=${{ github.event.pull_request.head.sha
+        }}\" >> $GITHUB_ENV\n  else\n    echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n\
+        \  fi\nfi\n"
     - name: Git checkout
       uses: actions/checkout@v4
       with:
         fetch-depth: 0
         ref: ${{ env.tested_commit }}
     - name: Cachix install
-      uses: cachix/install-nix-action@v27
+      uses: cachix/install-nix-action@v30
       with:
         nix_path: nixpkgs=channel:nixpkgs-unstable
     - name: Cachix setup math-comp
@@ -86,8 +86,8 @@ jobs:
         name: math-comp
     - id: stepCheck
       name: Checking presence of CI target mathcomp
-      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr\
-        \ bundle \"8.18\" --argstr job \"mathcomp\" \\\n   --dry-run 2>&1 > /dev/null)\n\
+      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr
+        bundle \"8.18\" --argstr job \"mathcomp\" \\\n   --dry-run 2>&1 > /dev/null)\n
         echo $nb_dry_run\necho status=$(echo $nb_dry_run | grep \"built:\" | sed \"\
         s/.*/built/\") >> $GITHUB_OUTPUT\n"
     - if: steps.stepCheck.outputs.status == 'built'
@@ -132,30 +132,30 @@ jobs:
     runs-on: ubuntu-latest
     steps:
     - name: Determine which commit to initially checkout
-      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"target_commit=${{\
-        \ github.sha }}\" >> $GITHUB_ENV\nelse\n  echo \"target_commit=${{ github.event.pull_request.head.sha\
-        \ }}\" >> $GITHUB_ENV\nfi\n"
+      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"target_commit=${{
+        github.sha }}\" >> $GITHUB_ENV\nelse\n  echo \"target_commit=${{ github.event.pull_request.head.sha
+        }}\" >> $GITHUB_ENV\nfi\n"
     - name: Git checkout
       uses: actions/checkout@v4
       with:
         fetch-depth: 0
         ref: ${{ env.target_commit }}
     - name: Determine which commit to test
-      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"tested_commit=${{\
-        \ github.sha }}\" >> $GITHUB_ENV\nelse\n  merge_commit=$(git ls-remote ${{\
-        \ github.event.repository.html_url }} refs/pull/${{ github.event.number }}/merge\
-        \ | cut -f1)\n  mergeable=$(git merge --no-commit --no-ff ${{ github.event.pull_request.base.sha\
-        \ }} > /dev/null 2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n\
-        \  if [ -z \"$merge_commit\" -o \"x$mergeable\" != \"x0\" ]; then\n    echo\
-        \ \"tested_commit=${{ github.event.pull_request.head.sha }}\" >> $GITHUB_ENV\n\
-        \  else\n    echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n  fi\nfi\n"
+      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"tested_commit=${{
+        github.sha }}\" >> $GITHUB_ENV\nelse\n  merge_commit=$(git ls-remote ${{ github.event.repository.html_url
+        }} refs/pull/${{ github.event.number }}/merge | cut -f1)\n  mergeable=$(git
+        merge --no-commit --no-ff ${{ github.event.pull_request.base.sha }} > /dev/null
+        2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n  if [ -z \"$merge_commit\"\
+        \ -o \"x$mergeable\" != \"x0\" ]; then\n    echo \"tested_commit=${{ github.event.pull_request.head.sha
+        }}\" >> $GITHUB_ENV\n  else\n    echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n\
+        \  fi\nfi\n"
     - name: Git checkout
       uses: actions/checkout@v4
       with:
         fetch-depth: 0
         ref: ${{ env.tested_commit }}
     - name: Cachix install
-      uses: cachix/install-nix-action@v27
+      uses: cachix/install-nix-action@v30
       with:
         nix_path: nixpkgs=channel:nixpkgs-unstable
     - name: Cachix setup math-comp
@@ -166,8 +166,8 @@ jobs:
         name: math-comp
     - id: stepCheck
       name: Checking presence of CI target mathcomp-cad
-      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr\
-        \ bundle \"8.18\" --argstr job \"mathcomp-cad\" \\\n   --dry-run 2>&1 > /dev/null)\n\
+      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr
+        bundle \"8.18\" --argstr job \"mathcomp-cad\" \\\n   --dry-run 2>&1 > /dev/null)\n
         echo $nb_dry_run\necho status=$(echo $nb_dry_run | grep \"built:\" | sed \"\
         s/.*/built/\") >> $GITHUB_OUTPUT\n"
     - if: steps.stepCheck.outputs.status == 'built'
@@ -223,7 +223,7 @@ jobs:
       run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.18" --argstr
         job "mathcomp-cad"
 name: Nix CI for bundle 8.18
-'on':
+on:
   pull_request:
     paths:
     - .github/workflows/nix-action-8.18.yml
diff --git a/.github/workflows/nix-action-8.19.yml b/.github/workflows/nix-action-8.19.yml
index 92098d7..3a46870 100644
--- a/.github/workflows/nix-action-8.19.yml
+++ b/.github/workflows/nix-action-8.19.yml
@@ -4,30 +4,30 @@ jobs:
     runs-on: ubuntu-latest
     steps:
     - name: Determine which commit to initially checkout
-      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"target_commit=${{\
-        \ github.sha }}\" >> $GITHUB_ENV\nelse\n  echo \"target_commit=${{ github.event.pull_request.head.sha\
-        \ }}\" >> $GITHUB_ENV\nfi\n"
+      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"target_commit=${{
+        github.sha }}\" >> $GITHUB_ENV\nelse\n  echo \"target_commit=${{ github.event.pull_request.head.sha
+        }}\" >> $GITHUB_ENV\nfi\n"
     - name: Git checkout
       uses: actions/checkout@v4
       with:
         fetch-depth: 0
         ref: ${{ env.target_commit }}
     - name: Determine which commit to test
-      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"tested_commit=${{\
-        \ github.sha }}\" >> $GITHUB_ENV\nelse\n  merge_commit=$(git ls-remote ${{\
-        \ github.event.repository.html_url }} refs/pull/${{ github.event.number }}/merge\
-        \ | cut -f1)\n  mergeable=$(git merge --no-commit --no-ff ${{ github.event.pull_request.base.sha\
-        \ }} > /dev/null 2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n\
-        \  if [ -z \"$merge_commit\" -o \"x$mergeable\" != \"x0\" ]; then\n    echo\
-        \ \"tested_commit=${{ github.event.pull_request.head.sha }}\" >> $GITHUB_ENV\n\
-        \  else\n    echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n  fi\nfi\n"
+      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"tested_commit=${{
+        github.sha }}\" >> $GITHUB_ENV\nelse\n  merge_commit=$(git ls-remote ${{ github.event.repository.html_url
+        }} refs/pull/${{ github.event.number }}/merge | cut -f1)\n  mergeable=$(git
+        merge --no-commit --no-ff ${{ github.event.pull_request.base.sha }} > /dev/null
+        2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n  if [ -z \"$merge_commit\"\
+        \ -o \"x$mergeable\" != \"x0\" ]; then\n    echo \"tested_commit=${{ github.event.pull_request.head.sha
+        }}\" >> $GITHUB_ENV\n  else\n    echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n\
+        \  fi\nfi\n"
     - name: Git checkout
       uses: actions/checkout@v4
       with:
         fetch-depth: 0
         ref: ${{ env.tested_commit }}
     - name: Cachix install
-      uses: cachix/install-nix-action@v27
+      uses: cachix/install-nix-action@v30
       with:
         nix_path: nixpkgs=channel:nixpkgs-unstable
     - name: Cachix setup math-comp
@@ -38,8 +38,8 @@ jobs:
         name: math-comp
     - id: stepCheck
       name: Checking presence of CI target coq
-      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr\
-        \ bundle \"8.19\" --argstr job \"coq\" \\\n   --dry-run 2>&1 > /dev/null)\n\
+      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr
+        bundle \"8.19\" --argstr job \"coq\" \\\n   --dry-run 2>&1 > /dev/null)\n
         echo $nb_dry_run\necho status=$(echo $nb_dry_run | grep \"built:\" | sed \"\
         s/.*/built/\") >> $GITHUB_OUTPUT\n"
     - if: steps.stepCheck.outputs.status == 'built'
@@ -52,30 +52,30 @@ jobs:
     runs-on: ubuntu-latest
     steps:
     - name: Determine which commit to initially checkout
-      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"target_commit=${{\
-        \ github.sha }}\" >> $GITHUB_ENV\nelse\n  echo \"target_commit=${{ github.event.pull_request.head.sha\
-        \ }}\" >> $GITHUB_ENV\nfi\n"
+      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"target_commit=${{
+        github.sha }}\" >> $GITHUB_ENV\nelse\n  echo \"target_commit=${{ github.event.pull_request.head.sha
+        }}\" >> $GITHUB_ENV\nfi\n"
     - name: Git checkout
       uses: actions/checkout@v4
       with:
         fetch-depth: 0
         ref: ${{ env.target_commit }}
     - name: Determine which commit to test
-      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"tested_commit=${{\
-        \ github.sha }}\" >> $GITHUB_ENV\nelse\n  merge_commit=$(git ls-remote ${{\
-        \ github.event.repository.html_url }} refs/pull/${{ github.event.number }}/merge\
-        \ | cut -f1)\n  mergeable=$(git merge --no-commit --no-ff ${{ github.event.pull_request.base.sha\
-        \ }} > /dev/null 2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n\
-        \  if [ -z \"$merge_commit\" -o \"x$mergeable\" != \"x0\" ]; then\n    echo\
-        \ \"tested_commit=${{ github.event.pull_request.head.sha }}\" >> $GITHUB_ENV\n\
-        \  else\n    echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n  fi\nfi\n"
+      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"tested_commit=${{
+        github.sha }}\" >> $GITHUB_ENV\nelse\n  merge_commit=$(git ls-remote ${{ github.event.repository.html_url
+        }} refs/pull/${{ github.event.number }}/merge | cut -f1)\n  mergeable=$(git
+        merge --no-commit --no-ff ${{ github.event.pull_request.base.sha }} > /dev/null
+        2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n  if [ -z \"$merge_commit\"\
+        \ -o \"x$mergeable\" != \"x0\" ]; then\n    echo \"tested_commit=${{ github.event.pull_request.head.sha
+        }}\" >> $GITHUB_ENV\n  else\n    echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n\
+        \  fi\nfi\n"
     - name: Git checkout
       uses: actions/checkout@v4
       with:
         fetch-depth: 0
         ref: ${{ env.tested_commit }}
     - name: Cachix install
-      uses: cachix/install-nix-action@v27
+      uses: cachix/install-nix-action@v30
       with:
         nix_path: nixpkgs=channel:nixpkgs-unstable
     - name: Cachix setup math-comp
@@ -86,8 +86,8 @@ jobs:
         name: math-comp
     - id: stepCheck
       name: Checking presence of CI target mathcomp
-      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr\
-        \ bundle \"8.19\" --argstr job \"mathcomp\" \\\n   --dry-run 2>&1 > /dev/null)\n\
+      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr
+        bundle \"8.19\" --argstr job \"mathcomp\" \\\n   --dry-run 2>&1 > /dev/null)\n
         echo $nb_dry_run\necho status=$(echo $nb_dry_run | grep \"built:\" | sed \"\
         s/.*/built/\") >> $GITHUB_OUTPUT\n"
     - if: steps.stepCheck.outputs.status == 'built'
@@ -132,30 +132,30 @@ jobs:
     runs-on: ubuntu-latest
     steps:
     - name: Determine which commit to initially checkout
-      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"target_commit=${{\
-        \ github.sha }}\" >> $GITHUB_ENV\nelse\n  echo \"target_commit=${{ github.event.pull_request.head.sha\
-        \ }}\" >> $GITHUB_ENV\nfi\n"
+      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"target_commit=${{
+        github.sha }}\" >> $GITHUB_ENV\nelse\n  echo \"target_commit=${{ github.event.pull_request.head.sha
+        }}\" >> $GITHUB_ENV\nfi\n"
     - name: Git checkout
       uses: actions/checkout@v4
       with:
         fetch-depth: 0
         ref: ${{ env.target_commit }}
     - name: Determine which commit to test
-      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"tested_commit=${{\
-        \ github.sha }}\" >> $GITHUB_ENV\nelse\n  merge_commit=$(git ls-remote ${{\
-        \ github.event.repository.html_url }} refs/pull/${{ github.event.number }}/merge\
-        \ | cut -f1)\n  mergeable=$(git merge --no-commit --no-ff ${{ github.event.pull_request.base.sha\
-        \ }} > /dev/null 2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n\
-        \  if [ -z \"$merge_commit\" -o \"x$mergeable\" != \"x0\" ]; then\n    echo\
-        \ \"tested_commit=${{ github.event.pull_request.head.sha }}\" >> $GITHUB_ENV\n\
-        \  else\n    echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n  fi\nfi\n"
+      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"tested_commit=${{
+        github.sha }}\" >> $GITHUB_ENV\nelse\n  merge_commit=$(git ls-remote ${{ github.event.repository.html_url
+        }} refs/pull/${{ github.event.number }}/merge | cut -f1)\n  mergeable=$(git
+        merge --no-commit --no-ff ${{ github.event.pull_request.base.sha }} > /dev/null
+        2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n  if [ -z \"$merge_commit\"\
+        \ -o \"x$mergeable\" != \"x0\" ]; then\n    echo \"tested_commit=${{ github.event.pull_request.head.sha
+        }}\" >> $GITHUB_ENV\n  else\n    echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n\
+        \  fi\nfi\n"
     - name: Git checkout
       uses: actions/checkout@v4
       with:
         fetch-depth: 0
         ref: ${{ env.tested_commit }}
     - name: Cachix install
-      uses: cachix/install-nix-action@v27
+      uses: cachix/install-nix-action@v30
       with:
         nix_path: nixpkgs=channel:nixpkgs-unstable
     - name: Cachix setup math-comp
@@ -166,8 +166,8 @@ jobs:
         name: math-comp
     - id: stepCheck
       name: Checking presence of CI target mathcomp-cad
-      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr\
-        \ bundle \"8.19\" --argstr job \"mathcomp-cad\" \\\n   --dry-run 2>&1 > /dev/null)\n\
+      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr
+        bundle \"8.19\" --argstr job \"mathcomp-cad\" \\\n   --dry-run 2>&1 > /dev/null)\n
         echo $nb_dry_run\necho status=$(echo $nb_dry_run | grep \"built:\" | sed \"\
         s/.*/built/\") >> $GITHUB_OUTPUT\n"
     - if: steps.stepCheck.outputs.status == 'built'
@@ -223,7 +223,7 @@ jobs:
       run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.19" --argstr
         job "mathcomp-cad"
 name: Nix CI for bundle 8.19
-'on':
+on:
   pull_request:
     paths:
     - .github/workflows/nix-action-8.19.yml
diff --git a/.github/workflows/nix-action-8.20.yml b/.github/workflows/nix-action-8.20.yml
index 873f390..b5b8f4a 100644
--- a/.github/workflows/nix-action-8.20.yml
+++ b/.github/workflows/nix-action-8.20.yml
@@ -4,30 +4,30 @@ jobs:
     runs-on: ubuntu-latest
     steps:
     - name: Determine which commit to initially checkout
-      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"target_commit=${{\
-        \ github.sha }}\" >> $GITHUB_ENV\nelse\n  echo \"target_commit=${{ github.event.pull_request.head.sha\
-        \ }}\" >> $GITHUB_ENV\nfi\n"
+      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"target_commit=${{
+        github.sha }}\" >> $GITHUB_ENV\nelse\n  echo \"target_commit=${{ github.event.pull_request.head.sha
+        }}\" >> $GITHUB_ENV\nfi\n"
     - name: Git checkout
       uses: actions/checkout@v4
       with:
         fetch-depth: 0
         ref: ${{ env.target_commit }}
     - name: Determine which commit to test
-      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"tested_commit=${{\
-        \ github.sha }}\" >> $GITHUB_ENV\nelse\n  merge_commit=$(git ls-remote ${{\
-        \ github.event.repository.html_url }} refs/pull/${{ github.event.number }}/merge\
-        \ | cut -f1)\n  mergeable=$(git merge --no-commit --no-ff ${{ github.event.pull_request.base.sha\
-        \ }} > /dev/null 2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n\
-        \  if [ -z \"$merge_commit\" -o \"x$mergeable\" != \"x0\" ]; then\n    echo\
-        \ \"tested_commit=${{ github.event.pull_request.head.sha }}\" >> $GITHUB_ENV\n\
-        \  else\n    echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n  fi\nfi\n"
+      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"tested_commit=${{
+        github.sha }}\" >> $GITHUB_ENV\nelse\n  merge_commit=$(git ls-remote ${{ github.event.repository.html_url
+        }} refs/pull/${{ github.event.number }}/merge | cut -f1)\n  mergeable=$(git
+        merge --no-commit --no-ff ${{ github.event.pull_request.base.sha }} > /dev/null
+        2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n  if [ -z \"$merge_commit\"\
+        \ -o \"x$mergeable\" != \"x0\" ]; then\n    echo \"tested_commit=${{ github.event.pull_request.head.sha
+        }}\" >> $GITHUB_ENV\n  else\n    echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n\
+        \  fi\nfi\n"
     - name: Git checkout
       uses: actions/checkout@v4
       with:
         fetch-depth: 0
         ref: ${{ env.tested_commit }}
     - name: Cachix install
-      uses: cachix/install-nix-action@v27
+      uses: cachix/install-nix-action@v30
       with:
         nix_path: nixpkgs=channel:nixpkgs-unstable
     - name: Cachix setup math-comp
@@ -38,8 +38,8 @@ jobs:
         name: math-comp
     - id: stepCheck
       name: Checking presence of CI target coq
-      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr\
-        \ bundle \"8.20\" --argstr job \"coq\" \\\n   --dry-run 2>&1 > /dev/null)\n\
+      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr
+        bundle \"8.20\" --argstr job \"coq\" \\\n   --dry-run 2>&1 > /dev/null)\n
         echo $nb_dry_run\necho status=$(echo $nb_dry_run | grep \"built:\" | sed \"\
         s/.*/built/\") >> $GITHUB_OUTPUT\n"
     - if: steps.stepCheck.outputs.status == 'built'
@@ -52,30 +52,30 @@ jobs:
     runs-on: ubuntu-latest
     steps:
     - name: Determine which commit to initially checkout
-      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"target_commit=${{\
-        \ github.sha }}\" >> $GITHUB_ENV\nelse\n  echo \"target_commit=${{ github.event.pull_request.head.sha\
-        \ }}\" >> $GITHUB_ENV\nfi\n"
+      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"target_commit=${{
+        github.sha }}\" >> $GITHUB_ENV\nelse\n  echo \"target_commit=${{ github.event.pull_request.head.sha
+        }}\" >> $GITHUB_ENV\nfi\n"
     - name: Git checkout
       uses: actions/checkout@v4
       with:
         fetch-depth: 0
         ref: ${{ env.target_commit }}
     - name: Determine which commit to test
-      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"tested_commit=${{\
-        \ github.sha }}\" >> $GITHUB_ENV\nelse\n  merge_commit=$(git ls-remote ${{\
-        \ github.event.repository.html_url }} refs/pull/${{ github.event.number }}/merge\
-        \ | cut -f1)\n  mergeable=$(git merge --no-commit --no-ff ${{ github.event.pull_request.base.sha\
-        \ }} > /dev/null 2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n\
-        \  if [ -z \"$merge_commit\" -o \"x$mergeable\" != \"x0\" ]; then\n    echo\
-        \ \"tested_commit=${{ github.event.pull_request.head.sha }}\" >> $GITHUB_ENV\n\
-        \  else\n    echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n  fi\nfi\n"
+      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"tested_commit=${{
+        github.sha }}\" >> $GITHUB_ENV\nelse\n  merge_commit=$(git ls-remote ${{ github.event.repository.html_url
+        }} refs/pull/${{ github.event.number }}/merge | cut -f1)\n  mergeable=$(git
+        merge --no-commit --no-ff ${{ github.event.pull_request.base.sha }} > /dev/null
+        2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n  if [ -z \"$merge_commit\"\
+        \ -o \"x$mergeable\" != \"x0\" ]; then\n    echo \"tested_commit=${{ github.event.pull_request.head.sha
+        }}\" >> $GITHUB_ENV\n  else\n    echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n\
+        \  fi\nfi\n"
     - name: Git checkout
       uses: actions/checkout@v4
       with:
         fetch-depth: 0
         ref: ${{ env.tested_commit }}
     - name: Cachix install
-      uses: cachix/install-nix-action@v27
+      uses: cachix/install-nix-action@v30
       with:
         nix_path: nixpkgs=channel:nixpkgs-unstable
     - name: Cachix setup math-comp
@@ -86,8 +86,8 @@ jobs:
         name: math-comp
     - id: stepCheck
       name: Checking presence of CI target mathcomp
-      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr\
-        \ bundle \"8.20\" --argstr job \"mathcomp\" \\\n   --dry-run 2>&1 > /dev/null)\n\
+      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr
+        bundle \"8.20\" --argstr job \"mathcomp\" \\\n   --dry-run 2>&1 > /dev/null)\n
         echo $nb_dry_run\necho status=$(echo $nb_dry_run | grep \"built:\" | sed \"\
         s/.*/built/\") >> $GITHUB_OUTPUT\n"
     - if: steps.stepCheck.outputs.status == 'built'
@@ -132,30 +132,30 @@ jobs:
     runs-on: ubuntu-latest
     steps:
     - name: Determine which commit to initially checkout
-      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"target_commit=${{\
-        \ github.sha }}\" >> $GITHUB_ENV\nelse\n  echo \"target_commit=${{ github.event.pull_request.head.sha\
-        \ }}\" >> $GITHUB_ENV\nfi\n"
+      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"target_commit=${{
+        github.sha }}\" >> $GITHUB_ENV\nelse\n  echo \"target_commit=${{ github.event.pull_request.head.sha
+        }}\" >> $GITHUB_ENV\nfi\n"
     - name: Git checkout
       uses: actions/checkout@v4
       with:
         fetch-depth: 0
         ref: ${{ env.target_commit }}
     - name: Determine which commit to test
-      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"tested_commit=${{\
-        \ github.sha }}\" >> $GITHUB_ENV\nelse\n  merge_commit=$(git ls-remote ${{\
-        \ github.event.repository.html_url }} refs/pull/${{ github.event.number }}/merge\
-        \ | cut -f1)\n  mergeable=$(git merge --no-commit --no-ff ${{ github.event.pull_request.base.sha\
-        \ }} > /dev/null 2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n\
-        \  if [ -z \"$merge_commit\" -o \"x$mergeable\" != \"x0\" ]; then\n    echo\
-        \ \"tested_commit=${{ github.event.pull_request.head.sha }}\" >> $GITHUB_ENV\n\
-        \  else\n    echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n  fi\nfi\n"
+      run: "if [ ${{ github.event_name }} = \"push\" ]; then\n  echo \"tested_commit=${{
+        github.sha }}\" >> $GITHUB_ENV\nelse\n  merge_commit=$(git ls-remote ${{ github.event.repository.html_url
+        }} refs/pull/${{ github.event.number }}/merge | cut -f1)\n  mergeable=$(git
+        merge --no-commit --no-ff ${{ github.event.pull_request.base.sha }} > /dev/null
+        2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n  if [ -z \"$merge_commit\"\
+        \ -o \"x$mergeable\" != \"x0\" ]; then\n    echo \"tested_commit=${{ github.event.pull_request.head.sha
+        }}\" >> $GITHUB_ENV\n  else\n    echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n\
+        \  fi\nfi\n"
     - name: Git checkout
       uses: actions/checkout@v4
       with:
         fetch-depth: 0
         ref: ${{ env.tested_commit }}
     - name: Cachix install
-      uses: cachix/install-nix-action@v27
+      uses: cachix/install-nix-action@v30
       with:
         nix_path: nixpkgs=channel:nixpkgs-unstable
     - name: Cachix setup math-comp
@@ -166,8 +166,8 @@ jobs:
         name: math-comp
     - id: stepCheck
       name: Checking presence of CI target mathcomp-cad
-      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr\
-        \ bundle \"8.20\" --argstr job \"mathcomp-cad\" \\\n   --dry-run 2>&1 > /dev/null)\n\
+      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr
+        bundle \"8.20\" --argstr job \"mathcomp-cad\" \\\n   --dry-run 2>&1 > /dev/null)\n
         echo $nb_dry_run\necho status=$(echo $nb_dry_run | grep \"built:\" | sed \"\
         s/.*/built/\") >> $GITHUB_OUTPUT\n"
     - if: steps.stepCheck.outputs.status == 'built'
@@ -223,7 +223,7 @@ jobs:
       run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
         job "mathcomp-cad"
 name: Nix CI for bundle 8.20
-'on':
+on:
   pull_request:
     paths:
     - .github/workflows/nix-action-8.20.yml
diff --git a/.nix/coq-nix-toolbox.nix b/.nix/coq-nix-toolbox.nix
index 95cb895..d131964 100644
--- a/.nix/coq-nix-toolbox.nix
+++ b/.nix/coq-nix-toolbox.nix
@@ -1 +1 @@
-"a996cd700733fdd54c96ef3a1147cd844fb12cf1"
+"3c14d6d7c3d948a65d42905a56019ce0f306622e"
diff --git a/LICENSE b/LICENSE
new file mode 100644
index 0000000..0a04128
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,165 @@
+                   GNU LESSER GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+
+  This version of the GNU Lesser General Public License incorporates
+the terms and conditions of version 3 of the GNU General Public
+License, supplemented by the additional permissions listed below.
+
+  0. Additional Definitions.
+
+  As used herein, "this License" refers to version 3 of the GNU Lesser
+General Public License, and the "GNU GPL" refers to version 3 of the GNU
+General Public License.
+
+  "The Library" refers to a covered work governed by this License,
+other than an Application or a Combined Work as defined below.
+
+  An "Application" is any work that makes use of an interface provided
+by the Library, but which is not otherwise based on the Library.
+Defining a subclass of a class defined by the Library is deemed a mode
+of using an interface provided by the Library.
+
+  A "Combined Work" is a work produced by combining or linking an
+Application with the Library.  The particular version of the Library
+with which the Combined Work was made is also called the "Linked
+Version".
+
+  The "Minimal Corresponding Source" for a Combined Work means the
+Corresponding Source for the Combined Work, excluding any source code
+for portions of the Combined Work that, considered in isolation, are
+based on the Application, and not on the Linked Version.
+
+  The "Corresponding Application Code" for a Combined Work means the
+object code and/or source code for the Application, including any data
+and utility programs needed for reproducing the Combined Work from the
+Application, but excluding the System Libraries of the Combined Work.
+
+  1. Exception to Section 3 of the GNU GPL.
+
+  You may convey a covered work under sections 3 and 4 of this License
+without being bound by section 3 of the GNU GPL.
+
+  2. Conveying Modified Versions.
+
+  If you modify a copy of the Library, and, in your modifications, a
+facility refers to a function or data to be supplied by an Application
+that uses the facility (other than as an argument passed when the
+facility is invoked), then you may convey a copy of the modified
+version:
+
+   a) under this License, provided that you make a good faith effort to
+   ensure that, in the event an Application does not supply the
+   function or data, the facility still operates, and performs
+   whatever part of its purpose remains meaningful, or
+
+   b) under the GNU GPL, with none of the additional permissions of
+   this License applicable to that copy.
+
+  3. Object Code Incorporating Material from Library Header Files.
+
+  The object code form of an Application may incorporate material from
+a header file that is part of the Library.  You may convey such object
+code under terms of your choice, provided that, if the incorporated
+material is not limited to numerical parameters, data structure
+layouts and accessors, or small macros, inline functions and templates
+(ten or fewer lines in length), you do both of the following:
+
+   a) Give prominent notice with each copy of the object code that the
+   Library is used in it and that the Library and its use are
+   covered by this License.
+
+   b) Accompany the object code with a copy of the GNU GPL and this license
+   document.
+
+  4. Combined Works.
+
+  You may convey a Combined Work under terms of your choice that,
+taken together, effectively do not restrict modification of the
+portions of the Library contained in the Combined Work and reverse
+engineering for debugging such modifications, if you also do each of
+the following:
+
+   a) Give prominent notice with each copy of the Combined Work that
+   the Library is used in it and that the Library and its use are
+   covered by this License.
+
+   b) Accompany the Combined Work with a copy of the GNU GPL and this license
+   document.
+
+   c) For a Combined Work that displays copyright notices during
+   execution, include the copyright notice for the Library among
+   these notices, as well as a reference directing the user to the
+   copies of the GNU GPL and this license document.
+
+   d) Do one of the following:
+
+       0) Convey the Minimal Corresponding Source under the terms of this
+       License, and the Corresponding Application Code in a form
+       suitable for, and under terms that permit, the user to
+       recombine or relink the Application with a modified version of
+       the Linked Version to produce a modified Combined Work, in the
+       manner specified by section 6 of the GNU GPL for conveying
+       Corresponding Source.
+
+       1) Use a suitable shared library mechanism for linking with the
+       Library.  A suitable mechanism is one that (a) uses at run time
+       a copy of the Library already present on the user's computer
+       system, and (b) will operate properly with a modified version
+       of the Library that is interface-compatible with the Linked
+       Version.
+
+   e) Provide Installation Information, but only if you would otherwise
+   be required to provide such information under section 6 of the
+   GNU GPL, and only to the extent that such information is
+   necessary to install and execute a modified version of the
+   Combined Work produced by recombining or relinking the
+   Application with a modified version of the Linked Version. (If
+   you use option 4d0, the Installation Information must accompany
+   the Minimal Corresponding Source and Corresponding Application
+   Code. If you use option 4d1, you must provide the Installation
+   Information in the manner specified by section 6 of the GNU GPL
+   for conveying Corresponding Source.)
+
+  5. Combined Libraries.
+
+  You may place library facilities that are a work based on the
+Library side by side in a single library together with other library
+facilities that are not Applications and are not covered by this
+License, and convey such a combined library under terms of your
+choice, if you do both of the following:
+
+   a) Accompany the combined library with a copy of the same work based
+   on the Library, uncombined with any other library facilities,
+   conveyed under the terms of this License.
+
+   b) Give prominent notice with the combined library that part of it
+   is a work based on the Library, and explaining where to find the
+   accompanying uncombined form of the same work.
+
+  6. Revised Versions of the GNU Lesser General Public License.
+
+  The Free Software Foundation may publish revised and/or new versions
+of the GNU Lesser General Public License from time to time. Such new
+versions will be similar in spirit to the present version, but may
+differ in detail to address new problems or concerns.
+
+  Each version is given a distinguishing version number. If the
+Library as you received it specifies that a certain numbered version
+of the GNU Lesser General Public License "or any later version"
+applies to it, you have the option of following the terms and
+conditions either of that published version or of any later version
+published by the Free Software Foundation. If the Library as you
+received it does not specify a version number of the GNU Lesser
+General Public License, you may choose any version of the GNU Lesser
+General Public License ever published by the Free Software Foundation.
+
+  If the Library as you received it specifies that a proxy can decide
+whether future versions of the GNU Lesser General Public License shall
+apply, that proxy's public statement of acceptance of any version is
+permanent authorization for you to choose that version for the
+Library.
diff --git a/README.md b/README.md
index 833826c..6fcccd0 100644
--- a/README.md
+++ b/README.md
@@ -1,38 +1,63 @@
-# cad
-Formalizing Cylindrical Algebraic Decomposition and related theories in mathcomp
+<!---
+This file was generated from `meta.yml`, please do not edit manually.
+Follow the instructions on https://github.com/coq-community/templates to regenerate.
+--->
+# Cylindical Algbebraic Decomposition
 
-# META
-- Compatible Coq versions: Coq 8.18 to 8.20 (or dev)
+[![Docker CI][docker-action-shield]][docker-action-link]
+
+[docker-action-shield]: https://github.com/math-comp/cad/actions/workflows/docker-action.yml/badge.svg?branch=master
+[docker-action-link]: https://github.com/math-comp/cad/actions/workflows/docker-action.yml
+
+
+
+
+This library contains a formal proof of Collins' Cylindical
+Aglebraic Decomposition, using the Mathematical Components Library.
+
+## Meta
+
+- Author(s):
+  - Cyril Cohen (initial)
+  - Boris Djalal (initial)
+  - Quentin Vermande (initial)
+- License: [GNU Lesser General Public License v3.0](LICENSE)
+- Compatible Coq versions: Coq 8.18 or later
 - Additional dependencies:
-	- MathComp ssreflect 2.2.0 or later
-	- MathComp fingroup 2.2.0 or later
-	- MathComp algebra 2.2.0 or later
-	- MathComp solvable 2.2.0 or later
-	- MathComp field 2.2.0 or later
-	- MathComp finmap 2.2.0 or later
-	- MathComp bigenough 2.2.0 or later
-	- MathComp multinomials 2.2.0 or later
-	- MathComp finmap 2.1.0 or later
-	- MathComp real-closed 2.0.1 or later
-	- MathComp classical 1.1.0 or later
-	- MathComp analysis 1.1.0 or later
-	- Hierarchy Builder 1.4.0 or later
-
-# Installation
-## With OPAM
-If you already have OPAM installed (a fresh or up to date version of opam 2 is required):
+  - [Hierarchy Builder >= 1.4.0 ](https://github.com/math-comp/hierarchy-builder)
+  - [MathComp ssreflect 2.2](https://math-comp.github.io)
+  - [MathComp algebra](https://math-comp.github.io)
+  - [MathComp fingroup](https://math-comp.github.io)
+  - [MathComp solvable](https://math-comp.github.io)
+  - [MathComp field](https://math-comp.github.io)
+  - [MathComp bigenough 1.0.1 or later](https://github.com/math-comp/bigenough)
+  - [MathComp bigenough 1.0.1 or later](https://github.com/math-comp/bigenough)
+  - [MathComp multinomials 2.2.0 or later](https://github.com/math-comp/multninomials)
+  - [MathComp real-closed 2.0.1 or later](https://github.com/math-comp/real-closed)
+  - [MathComp classical 1.1.0 or later](https://github.com/math-comp/analysis)
+  - [MathComp analysis 1.1.0 or later](https://github.com/math-comp/analysis)
+- Coq namespace: `SemiAlgebraic`
+- Related publication(s):
+  - [A Constructive Formalisation of Semi-algebraic Sets and Functions](https://hal.inria.fr/hal-01643919) doi:[10.1145/3167099](https://doi.org/10.1145/3167099)
 
-```
+## Building and installation instructions
+
+The easiest way to install the latest released version of Cylindical Algbebraic Decomposition
+is via [OPAM](https://opam.ocaml.org/doc/Install.html):
+
+```shell
 opam repo add coq-released https://coq.inria.fr/opam/released
 opam install coq-mathcomp-cad
 ```
 
-## Manual installation
-To build and install manually, make sure the dependencies are met and do 
+To instead build and install manually, do:
 
-```
+``` shell
 git clone https://github.com/math-comp/cad.git
 cd cad
 make   # or make -j <number-of-cores-on-your-machine> 
 make install
 ```
+
+
+
diff --git a/_CoqProject b/_CoqProject
index 2d9eae3..5b7cdeb 100644
--- a/_CoqProject
+++ b/_CoqProject
@@ -1,12 +1,12 @@
-extra_ssr.v
-subresultant.v
-auxresults.v
-formula.v
-continuity_roots.v
-semialgebraic.v
-topology.v
-cylinder.v
+theories/extra_ssr.v
+theories/subresultant.v
+theories/auxresults.v
+theories/formula.v
+theories/continuity_roots.v
+theories/semialgebraic.v
+theories/topology.v
+theories/cylinder.v
 
--R "." SemiAlgebraic
+-R theories SemiAlgebraic
 
 
diff --git a/coq-mathcomp-cad.opam b/coq-mathcomp-cad.opam
new file mode 100644
index 0000000..8d5a8ce
--- /dev/null
+++ b/coq-mathcomp-cad.opam
@@ -0,0 +1,44 @@
+# This file was generated from `meta.yml`, please do not edit manually.
+# Follow the instructions on https://github.com/coq-community/templates to regenerate.
+
+opam-version: "2.0"
+maintainer: "Cyril Cohen <cyril.cohen@inria.fr>"
+version: "dev"
+
+homepage: "https://github.com/math-comp/cad"
+dev-repo: "git+https://github.com/math-comp/cad.git"
+bug-reports: "https://github.com/math-comp/cad/issues"
+license: "LGPL-3.0-or-later"
+
+synopsis: "Formal Proof of Cylindrical Algebraic Decomposition"
+description: """
+This library contains a formal proof of Collins' Cylindical
+Aglebraic Decomposition, using the Mathematical Components Library."""
+
+build: [make "-j%{jobs}%"]
+install: [make "install"]
+depends: [
+  "coq" {>= "8.18"}
+  "coq-hierarchy-builder" 
+  "coq-mathcomp-ssreflect" {= "2.2.0 "}
+  "coq-mathcomp-algebra" 
+  "coq-mathcomp-fingroup" 
+  "coq-mathcomp-solvable" 
+  "coq-mathcomp-field" 
+  "coq-mathcomp-bigenough" {>= "1.0.1"}
+  "coq-mathcomp-finmap" {>= "1.0.1"}
+  "coq-mathcomp-multinomials" {>= "2.2.0"}
+  "coq-mathcomp-real-closed" {>= "2.0.1"}
+  "coq-mathcomp-classical" {>= "1.1.0"}
+  "coq-mathcomp-analysis" {>= "1.1.0"}
+]
+
+tags: [
+  "keyword:CAD"
+  "logpath:SemiAlgebraic"
+]
+authors: [
+  "Cyril Cohen"
+  "Boris Djalal"
+  "Quentin Vermande"
+]
diff --git a/meta.yml b/meta.yml
new file mode 100644
index 0000000..34e5f56
--- /dev/null
+++ b/meta.yml
@@ -0,0 +1,112 @@
+fullname: Cylindical Algbebraic Decomposition
+shortname: cad
+organization: math-comp
+opam_name: coq-mathcomp-cad
+community: false
+action: true
+coqdoc: false
+
+synopsis: >-
+  Formal Proof of Cylindrical Algebraic Decomposition
+description: |-
+  This library contains a formal proof of Collins' Cylindical
+  Aglebraic Decomposition, using the Mathematical Components Library.
+
+publications:
+- pub_url: https://hal.inria.fr/hal-01643919
+  pub_title: "A Constructive Formalisation of Semi-algebraic Sets and Functions"
+  pub_doi: 10.1145/3167099
+
+authors:
+- name: Cyril Cohen
+  initial: true
+- name: Boris Djalal
+  initial: initial
+- name: Quentin Vermande
+  initial: initial
+
+opam-file-maintainer: Cyril Cohen <cyril.cohen@inria.fr>
+
+opam-file-version: dev
+
+license:
+  fullname: GNU Lesser General Public License v3.0
+  identifier: LGPL-3.0-or-later
+  file: LICENSE
+
+supported_coq_versions:
+  text: Coq 8.18 or later
+  opam: '{>= "8.18"}'
+
+tested_coq_opam_versions:
+- version: '2.2.0-coq-8.18'
+  repo: 'mathcomp/mathcomp'
+- version: '2.2.0-coq-8.19'
+  repo: 'mathcomp/mathcomp'
+- version: '2.2.0-coq-8.20'
+  repo: 'mathcomp/mathcomp'
+
+dependencies:
+- opam:
+    name: coq-hierarchy-builder
+  description: |-
+    [Hierarchy Builder >= 1.4.0 ](https://github.com/math-comp/hierarchy-builder)
+- opam:
+    name: coq-mathcomp-ssreflect
+    version: '{= "2.2.0 "}'
+  description: |-
+    [MathComp ssreflect 2.2](https://math-comp.github.io)
+- opam:
+    name: coq-mathcomp-algebra
+  description: |-
+    [MathComp algebra](https://math-comp.github.io)
+- opam:
+    name: coq-mathcomp-fingroup
+  description: |-
+    [MathComp fingroup](https://math-comp.github.io)
+- opam:
+    name: coq-mathcomp-solvable
+  description: |-
+    [MathComp solvable](https://math-comp.github.io)
+- opam:
+    name: coq-mathcomp-field
+  description: |-
+    [MathComp field](https://math-comp.github.io)
+- opam:
+    name: coq-mathcomp-bigenough
+    version: '{>= "1.0.1"}'
+  description: |-
+    [MathComp bigenough 1.0.1 or later](https://github.com/math-comp/bigenough)
+- opam:
+    name: coq-mathcomp-finmap
+    version: '{>= "1.0.1"}'
+  description: |-
+    [MathComp bigenough 1.0.1 or later](https://github.com/math-comp/bigenough)
+- opam:
+    name: coq-mathcomp-multinomials
+    version: '{>= "2.2.0"}'
+  description: |-
+    [MathComp multinomials 2.2.0 or later](https://github.com/math-comp/multninomials)
+- opam:
+    name: coq-mathcomp-real-closed
+    version: '{>= "2.0.1"}'
+  description: |-
+    [MathComp real-closed 2.0.1 or later](https://github.com/math-comp/real-closed)
+- opam:
+    name: coq-mathcomp-classical
+    version: '{>= "1.1.0"}'
+  description: |-
+    [MathComp classical 1.1.0 or later](https://github.com/math-comp/analysis)
+- opam:
+    name: coq-mathcomp-analysis
+    version: '{>= "1.1.0"}'
+  description: |-
+    [MathComp analysis 1.1.0 or later](https://github.com/math-comp/analysis)
+
+
+namespace: SemiAlgebraic
+
+keywords:
+- name: CAD
+
+documentation: |-
diff --git a/auxresults.v b/theories/auxresults.v
similarity index 99%
rename from auxresults.v
rename to theories/auxresults.v
index 89240fb..648cc6c 100644
--- a/auxresults.v
+++ b/theories/auxresults.v
@@ -1,7 +1,8 @@
 (* (c) Copyright Microsoft Corporation and Inria. All rights reserved. *)
 From HB Require Import structures.
 From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
-From mathcomp Require Import order fintype generic_quotient path ssrint.
+From mathcomp Require Import order fintype generic_quotient ssrint.
+From mathcomp.ssreflect Require Import path.
 From mathcomp Require Import div tuple bigop ssralg ssrnum matrix poly polydiv.
 From mathcomp Require Import interval finmap mpoly polyorder polyrcf normedtype.
 From mathcomp Require Import complex classical_sets topology qe_rcf_th.
diff --git a/continuity_roots.v b/theories/continuity_roots.v
similarity index 100%
rename from continuity_roots.v
rename to theories/continuity_roots.v
diff --git a/cylinder.v b/theories/cylinder.v
similarity index 99%
rename from cylinder.v
rename to theories/cylinder.v
index c041054..20b7129 100644
--- a/cylinder.v
+++ b/theories/cylinder.v
@@ -1,6 +1,7 @@
 From mathcomp Require Import freeg ssreflect ssrfun ssrbool eqtype choice seq.
 From mathcomp Require Import ssrnat prime binomial bigop tuple order fintype.
-From mathcomp Require Import finfun path ssralg ssrnum ssrint poly matrix.
+From mathcomp Require Import finfun ssralg ssrnum ssrint poly matrix.
+From mathcomp.ssreflect Require Import path.
 From mathcomp Require Import finmap mpoly complex interval.
 From mathcomp Require Import polydiv polyrcf polyorder qe_rcf qe_rcf_th.
 
diff --git a/extra_ssr.v b/theories/extra_ssr.v
similarity index 100%
rename from extra_ssr.v
rename to theories/extra_ssr.v
diff --git a/formula.v b/theories/formula.v
similarity index 100%
rename from formula.v
rename to theories/formula.v
diff --git a/semialgebraic.v b/theories/semialgebraic.v
similarity index 99%
rename from semialgebraic.v
rename to theories/semialgebraic.v
index 018b4c6..a50cd5f 100644
--- a/semialgebraic.v
+++ b/theories/semialgebraic.v
@@ -29,7 +29,8 @@ Require Import ZArith Init.
 
 From HB Require Import structures.
 Require Import mathcomp.ssreflect.ssreflect.
-From mathcomp Require Import ssrfun ssrbool eqtype ssrnat seq choice path.
+From mathcomp Require Import ssrfun ssrbool eqtype ssrnat seq choice.
+From mathcomp.ssreflect Require Import path.
 From mathcomp Require Import fintype div tuple finfun generic_quotient bigop.
 From mathcomp Require Import finset perm ssralg ssrint poly polydiv ssrnum.
 From mathcomp Require Import mxpoly binomial interval finalg complex zmodp.
diff --git a/subresultant.v b/theories/subresultant.v
similarity index 100%
rename from subresultant.v
rename to theories/subresultant.v
diff --git a/topology.v b/theories/topology.v
similarity index 99%
rename from topology.v
rename to theories/topology.v
index 8dba7d8..511c5ea 100644
--- a/topology.v
+++ b/theories/topology.v
@@ -1,5 +1,8 @@
-From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice seq ssrnat bigop fintype finfun order ssralg ssrnum poly polydiv complex polyorder.
-From mathcomp Require Import matrix topology normedtype classical_sets interval.
+From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice seq.
+From mathcomp.ssreflect Require Import path.
+From mathcomp Require Import ssrnat bigop fintype finfun order ssralg ssrnum.
+From mathcomp Require Import poly polydiv complex polyorder matrix topology.
+From mathcomp Require Import  normedtype classical_sets interval.
 Require Import auxresults semialgebraic.
 
 Set Implicit Arguments.
@@ -494,7 +497,8 @@ case: m => [|m].
   suff ->: y = x by rewrite inE.
   by apply/rowP; case.
 case: n => [|n].
-  apply/(eq_continuous (f:=fun=> 0)); last exact/cst_continuous.
+  suff /eq_continuous : (fun=> 0) =1 SAselect R 0 m.+1 s.
+    by apply; exact/cst_continuous.
   move=> x; rewrite SAselectE; apply/rowP => i.
   by rewrite !mxE nth_default// size_ngraph.
 apply/continuousP => /= a; rewrite -open_subspace_setT => /open_subspace_ballP/= aopen.