chore: Fix build task names and check lake #6

	name: deploy-docs

	# Run this when the master or main branch changes
	on:
	push:
	branches:
	- main
	- doc/main

	# This job installs dependencies, builds the book, and pushes it to `gh-pages`
	jobs:
	deploy-book:
	runs-on: ubuntu-latest
	permissions:
	pages: write
	id-token: write
	steps:
	- uses: actions/checkout@v3

	# Install dependencies
	- name: Set up Python 3.11
	uses: actions/setup-python@v4
	with:
	python-version: 3.11

	- name: Install elan
	run: \|
	set -o pipefail
	curl -sSfL https://github.com/leanprover/elan/releases/download/v3.1.1/elan-x86_64-unknown-linux-gnu.tar.gz \| tar xz
	./elan-init -y --default-toolchain none
	echo "$HOME/.elan/bin" >> "${GITHUB_PATH}"

	- name: Print lean and lake versions
	run: \|
	lake --version

	- name: Install poetry
	run: \|
	pip install poetry
	poetry install --only doc

	- name: Build documentations
	run: \|
	poetry run jupyter-book build docs

	# Upload the book's HTML as an artifact
	- name: Upload artifact
	uses: actions/upload-pages-artifact@v2
	with:
	path: "docs/_build/html"

	# Deploy the book's HTML to GitHub Pages
	- name: Deploy to GitHub Pages
	id: deployment
	uses: actions/deploy-pages@v2

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