diff --git a/.github/workflows/nix-action-default.yml b/.github/workflows/nix-action-default.yml
new file mode 100644
index 0000000..c2e55c8
--- /dev/null
+++ b/.github/workflows/nix-action-default.yml
@@ -0,0 +1,173 @@
+jobs:
+  coq:
+    needs: []
+    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"
+    - name: Git checkout
+      uses: actions/checkout@v3
+      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"
+    - name: Git checkout
+      uses: actions/checkout@v3
+      with:
+        fetch-depth: 0
+        ref: ${{ env.tested_commit }}
+    - name: Cachix install
+      uses: cachix/install-nix-action@v20
+      with:
+        nix_path: nixpkgs=channel:nixpkgs-unstable
+    - name: Cachix setup coq
+      uses: cachix/cachix-action@v12
+      with:
+        extraPullNames: coq-community, math-comp
+        name: coq
+    - id: stepCheck
+      name: Checking presence of CI target coq
+      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr\
+        \ bundle \"default\" --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'
+      name: Building/fetching current CI target
+      run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "default"
+        --argstr job "coq"
+  coq-elpi:
+    needs:
+    - coq
+    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"
+    - name: Git checkout
+      uses: actions/checkout@v3
+      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"
+    - name: Git checkout
+      uses: actions/checkout@v3
+      with:
+        fetch-depth: 0
+        ref: ${{ env.tested_commit }}
+    - name: Cachix install
+      uses: cachix/install-nix-action@v20
+      with:
+        nix_path: nixpkgs=channel:nixpkgs-unstable
+    - name: Cachix setup coq
+      uses: cachix/cachix-action@v12
+      with:
+        extraPullNames: coq-community, math-comp
+        name: coq
+    - id: stepCheck
+      name: Checking presence of CI target coq-elpi
+      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr\
+        \ bundle \"default\" --argstr job \"coq-elpi\" \\\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'
+      name: 'Building/fetching previous CI target: coq'
+      run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "default"
+        --argstr job "coq"
+    - if: steps.stepCheck.outputs.status == 'built'
+      name: Building/fetching current CI target
+      run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "default"
+        --argstr job "coq-elpi"
+  trocq:
+    needs:
+    - coq
+    - coq-elpi
+    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"
+    - name: Git checkout
+      uses: actions/checkout@v3
+      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"
+    - name: Git checkout
+      uses: actions/checkout@v3
+      with:
+        fetch-depth: 0
+        ref: ${{ env.tested_commit }}
+    - name: Cachix install
+      uses: cachix/install-nix-action@v20
+      with:
+        nix_path: nixpkgs=channel:nixpkgs-unstable
+    - name: Cachix setup coq
+      uses: cachix/cachix-action@v12
+      with:
+        extraPullNames: coq-community, math-comp
+        name: coq
+    - id: stepCheck
+      name: Checking presence of CI target trocq
+      run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n   --argstr\
+        \ bundle \"default\" --argstr job \"trocq\" \\\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'
+      name: 'Building/fetching previous CI target: coq'
+      run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "default"
+        --argstr job "coq"
+    - if: steps.stepCheck.outputs.status == 'built'
+      name: 'Building/fetching previous CI target: HoTT'
+      run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "default"
+        --argstr job "HoTT"
+    - if: steps.stepCheck.outputs.status == 'built'
+      name: 'Building/fetching previous CI target: coq-elpi'
+      run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "default"
+        --argstr job "coq-elpi"
+    - if: steps.stepCheck.outputs.status == 'built'
+      name: Building/fetching current CI target
+      run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "default"
+        --argstr job "trocq"
+name: Nix CI for bundle default
+'on':
+  pull_request:
+    paths:
+    - .github/workflows/nix-action-default.yml
+  pull_request_target:
+    paths-ignore:
+    - .github/workflows/nix-action-default.yml
+    types:
+    - opened
+    - synchronize
+    - reopened
+  push:
+    branches:
+    - master
diff --git a/.nix/coq-nix-toolbox.nix b/.nix/coq-nix-toolbox.nix
index 60b452b..c869a31 100644
--- a/.nix/coq-nix-toolbox.nix
+++ b/.nix/coq-nix-toolbox.nix
@@ -1 +1 @@
-"f72eef6033e0abc9fa06f94fe718d8aa9c0d031a"
+"447fd9da2820c66dee263a327d62f3f3e9da2688"