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https://github.com/SinTan1729/lean-talk-sp24.git
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.gitignore
vendored
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.gitignore
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/.lake
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.directory
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3
Lean Talk SP24.lean
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Lean Talk SP24.lean
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-- This module serves as the root of the `«Lean Talk SP24»` library.
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-- Import modules here that should be built as part of the library.
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import «Lean Talk SP24».basics
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59
Lean Talk SP24/basics.lean
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59
Lean Talk SP24/basics.lean
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import Mathlib.Data.Nat.Basic
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import Mathlib.Data.Nat.Parity
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import Mathlib.Tactic
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open Nat
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-- Obligatory Hello World
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#eval "Hello world!"
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-- These are pieces of data.
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#check 2 + 2
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def f (x : ℕ) :=
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x + 3
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#check f
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-- These are propositions, of type `Prop`.
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#check 2 + 2 = 4
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def FermatLastTheorem :=
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∀ x y z n : ℕ, n > 2 ∧ x * y * z ≠ 0 → x ^ n + y ^ n ≠ z ^ n
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#check FermatLastTheorem
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-- These are proofs of propositions.
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theorem easy : 2 + 2 = 4 :=
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rfl
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#check easy
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theorem hard : FermatLastTheorem :=
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sorry
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#check hard
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-- Here are some proofs.
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example : ∀ m n : Nat, Even n → Even (m * n) := fun m n ⟨k, (hk : n = k + k)⟩ =>
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have hmn : m * n = m * k + m * k := by rw [hk, mul_add]
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show ∃ l, m * n = l + l from ⟨_, hmn⟩
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example : ∀ m n : Nat, Even n → Even (m * n) :=
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fun m n ⟨k, hk⟩ => ⟨m * k, by rw [hk, mul_add]⟩
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example : ∀ m n : Nat, Even n → Even (m * n) := by
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-- say m and n are natural numbers, and assume n=2*k
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rintro m n ⟨k, hk⟩
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-- We need to prove m*n is twice a natural number. Let's show it's twice m*k.
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use m * k
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-- substitute in for n
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rw [hk]
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-- and now it's obvious
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ring
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example : ∀ m n : Nat, Even n → Even (m * n) := by
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rintro m n ⟨k, hk⟩; use m * k; rw [hk]; ring
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example : ∀ m n : Nat, Even n → Even (m * n) := by
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intros; simp [*, parity_simps]
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lake-manifest.json
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{"version": 7,
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"packagesDir": ".lake/packages",
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"packages":
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[{"url": "https://github.com/leanprover/std4",
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"type": "git",
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"subDir": null,
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"rev": "276953b13323ca151939eafaaec9129bf7970306",
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"name": "std",
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"manifestFile": "lake-manifest.json",
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"inputRev": "main",
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"inherited": true,
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"configFile": "lakefile.lean"},
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{"url": "https://github.com/leanprover-community/quote4",
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"type": "git",
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"subDir": null,
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"rev": "1c88406514a636d241903e2e288d21dc6d861e01",
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"name": "Qq",
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"manifestFile": "lake-manifest.json",
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"inputRev": "master",
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"inherited": true,
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"configFile": "lakefile.lean"},
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{"url": "https://github.com/leanprover-community/aesop",
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"type": "git",
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"subDir": null,
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"rev": "6beed82dcfbb7731d173cd517675df27d62ad0f4",
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"name": "aesop",
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"manifestFile": "lake-manifest.json",
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"inputRev": "master",
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"inherited": true,
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"configFile": "lakefile.lean"},
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{"url": "https://github.com/leanprover-community/ProofWidgets4",
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"type": "git",
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"subDir": null,
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"rev": "af1e86cf7a37389632a02f4a111e6b501b2b818f",
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"name": "proofwidgets",
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"manifestFile": "lake-manifest.json",
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"inputRev": "v0.0.27",
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"inherited": true,
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"configFile": "lakefile.lean"},
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{"url": "https://github.com/leanprover/lean4-cli",
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"type": "git",
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"subDir": null,
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"rev": "a751d21d4b68c999accb6fc5d960538af26ad5ec",
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"name": "Cli",
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"manifestFile": "lake-manifest.json",
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"inputRev": "main",
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"inherited": true,
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"configFile": "lakefile.lean"},
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{"url": "https://github.com/leanprover-community/import-graph.git",
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"type": "git",
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"subDir": null,
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"rev": "8079d2d1d0e073bde42eab159c24f4c2d0d3a871",
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"name": "importGraph",
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"manifestFile": "lake-manifest.json",
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"inputRev": "main",
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"inherited": true,
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"configFile": "lakefile.lean"},
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{"url": "https://github.com/leanprover-community/mathlib4.git",
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"type": "git",
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"subDir": null,
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"rev": "328b7ecbc986507635abf725bbed4da70e418298",
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"name": "mathlib",
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"manifestFile": "lake-manifest.json",
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"inputRev": null,
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"inherited": false,
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"configFile": "lakefile.lean"}],
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"name": "«Lean Talk SP24»",
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"lakeDir": ".lake"}
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17
lakefile.lean
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17
lakefile.lean
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import Lake
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open Lake DSL
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package «Lean Talk SP24» where
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-- Settings applied to both builds and interactive editing
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leanOptions := #[
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⟨`pp.unicode.fun, true⟩, -- pretty-prints `fun a ↦ b`
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⟨`pp.proofs.withType, false⟩
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]
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-- add any additional package configuration options here
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require mathlib from git
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"https://github.com/leanprover-community/mathlib4.git"
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@[default_target]
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lean_lib «Lean Talk SP24» where
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-- add any library configuration options here
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1
lean-toolchain
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1
lean-toolchain
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leanprover/lean4:v4.6.0-rc1
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