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Try doing some basic maths questions in the Lean Theorem Prover. Functions, real numbers, equivalence relations and groups. Click on README.md and then on "Open in CoCalc with one click".

Project: Xena
Views: 18536
License: APACHE
/-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import tactic.tidy

open tactic

namespace tidy.test

meta def interactive_simp := `[simp]

def tidy_test_0 : ∀ x : unit, x = unit.star :=
begin
  success_if_fail { chain [ interactive_simp ] },
  intro1,
  induction x,
  refl
end
def tidy_test_1 (a : string) : ∀ x : unit, x = unit.star :=
begin
  tidy -- intros x, exact dec_trivial
end

structure A :=
(z : ℕ)

structure B :=
(a : A)
(aa : a.z = 0)

structure C :=
(a : A)
(b : B)
(ab : a.z = b.a.z)

structure D :=
(a : B)
(b : C)
(ab : a.a.z = b.a.z)

open tactic

def d : D :=
begin
  tidy,
  -- /- obviously says -/ fsplit, work_on_goal 0 { fsplit, work_on_goal 0 { fsplit }, work_on_goal 1 { refl } }, work_on_goal 0 { fsplit, work_on_goal 0 { fsplit }, work_on_goal 1 { fsplit, work_on_goal 0 { fsplit }, work_on_goal 1 { refl } }, work_on_goal 1 { refl } }, refl
end.

def f : unit → unit → unit := by tidy -- intros a a_1, cases a_1, cases a, fsplit

def g (P Q : Prop) (p : P) (h : P ↔ Q) : Q := by tidy

end tidy.test