update workflow files and readme

.devcontainer/Dockerfile

@@ -2,21 +2,27 @@ FROM node:20
 
 WORKDIR /
 
-ENV ELAN_HOME=/usr/local/elan \
-  PATH=/usr/local/elan/bin:$PATH \
-  LEAN_VERSION=leanprover/lean4:v4.1.0
-  # TODO: read toolchain from `lean-toolchain`
-
-SHELL ["/bin/bash", "-euxo", "pipefail", "-c"]
-
-RUN curl https://raw.githubusercontent.com/leanprover/elan/master/elan-init.sh -sSf | sh -s -- -y --no-modify-path --default-toolchain $LEAN_VERSION; \
-  chmod -R a+w $ELAN_HOME; \
-  elan --version; \
-  lean --version; \
-  leanc --version; \
-  lake --version;
+COPY ./lean-toolchain /lean-toolchain
 
 USER node
 
 WORKDIR /home/node
-RUN git clone https://github.com/leanprover-community/lean4game.git
+
+RUN export LEAN_VERSION="$(cat /lean-toolchain | grep -oE '[^:]+$')" && git clone --depth 1 --branch $LEAN_VERSION https://github.com/leanprover-community/lean4game.git
+
+WORKDIR /
+
+USER root
+
+ENV ELAN_HOME=/usr/local/elan \
+  PATH=/usr/local/elan/bin:$PATH
+
+SHELL ["/bin/bash", "-euxo", "pipefail", "-c"]
+
+RUN export LEAN_VERSION="$(cat /lean-toolchain)" && \
+  curl https://raw.githubusercontent.com/leanprover/elan/master/elan-init.sh -sSf | sh -s -- -y --no-modify-path --default-toolchain $LEAN_VERSION; \
+    chmod -R a+w $ELAN_HOME; \
+    elan --version; \
+    lean --version; \
+    leanc --version; \
+    lake --version;

.devcontainer/devcontainer.json

@@ -13,9 +13,9 @@
   "overrideCommand": true,
   "onCreateCommand": {
     "npm_install": "(cd ~/lean4game && npm install)",
-    "lake_build": "(cd ~/game && lake update && lake exe cache get && lake build)"
+    "lake_build": "(cd ~/game && lake clean && lake exe cache get && lake build)"
   },
-  "postStartCommand": "cd ~/lean4game && export LEAN4GAME_SINGLE_GAME=true && npm start",
+  "postStartCommand": "cd ~/lean4game && export VITE_LEAN4GAME_SINGLE=true && npm start",
   "customizations": {
     "vscode": {
       "settings": {

.devcontainer/docker-compose.yml

@@ -3,8 +3,8 @@ version: "3.9"
 services:
   game:
     build:
-      context: .
-      dockerfile: Dockerfile
+      context: ..
+      dockerfile: .devcontainer/Dockerfile
     volumes:
       - ..:/home/node/game
     ports: