diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 61cfc52..3705eb4 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -5,20 +5,49 @@ on:
 name: CI
 
 jobs:
-  update_lean_xyz_branch_and_build:
-    runs-on: ubuntu-latest
-    name: Update lean-x.y.z branch and build project
+  build:
+    strategy:
+      matrix:
+        include:
+          - name: Linux
+            os: ubuntu-latest
+          - name: Windows
+            os: windows-latest
+          - name: macOS
+            os: macos-latest
+
+    name: ${{ matrix.name }}
+    runs-on: ${{ matrix.os }}
     steps:
+      - uses: actions/checkout@v3
+
+      - name: Setup elan toolchain on Linux or macOS
+        if: matrix.os == 'ubuntu-latest' || matrix.os == 'macos-latest'
+        run: |
+          curl -O --location https://raw.githubusercontent.com/leanprover/elan/master/elan-init.sh
+          chmod u+x elan-init.sh
+          ./elan-init.sh -y --default-toolchain leanprover/lean4:nightly
+          echo "Adding location $HOME/.elan/bin to PATH..."
+          echo "$HOME/.elan/bin" >> $GITHUB_PATH
 
-    - name: checkout project
-      uses: actions/checkout@v2
-      with:
-        fetch-depth: 0
+      - name: Setup elan toolchain on Windows
+        if: matrix.os == 'windows-latest'
+        shell: pwsh
+        run: |
+          curl -O --location https://raw.githubusercontent.com/leanprover/elan/master/elan-init.ps1
+          .\elan-init.ps1 -NoPrompt 1 -DefaultToolchain leanprover/lean4:nightly
+          echo "Adding location $HOME\.elan\bin to PATH..."
+          echo "$HOME\.elan\bin" >> $env:GITHUB_PATH
 
-    - name: update branch
-      if: github.ref == 'refs/heads/master'
-      uses: leanprover-contrib/update-versions-action@master
+      - name: Test elan & lean are working
+        run: |
+          elan --version
+          lean --version
 
-    - name: build project
-      uses: leanprover-contrib/lean-build-action@master
+      - name: Build everything
+        run: |
+          lake build
 
+      - name: Run the test
+        run: |
+          lake exe test