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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
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/-
Copyright (c) 2018 Keeley Hoek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Keeley Hoek
-/
import tactic.converter.interactive
import tactic.ring

example : 0 + 0 = 0 :=
begin
  conv_lhs {erw [add_zero]}
end

example : 0 + 0 = 0 :=
begin
  conv_lhs {simp}
end

example : 0 = 0 + 0 :=
begin
  conv_rhs {simp}
end

-- Example with ring discharging the goal
example : 22 + 7 * 4 + 3 * 8 = 0 + 7 * 4 + 46 :=
begin
  conv { ring, },
end

-- Example with ring failing to discharge, to normalizing the goal
example : (22 + 7 * 4 + 3 * 8 = 0 + 7 * 4 + 47) = (74 = 75) :=
begin
  conv { ring, },
end

-- Example with ring discharging the goal
example (x : ℕ) : 22 + 7 * x + 3 * 8 = 0 + 7 * x + 46 :=
begin
  conv { ring, },
end

-- Example with ring failing to discharge, to normalizing the goal
example (x : ℕ) : (22 + 7 * x + 3 * 8 = 0 + 7 * x + 46 + 1)
                    = (7 * x + 46 = 7 * x + 47) :=
begin
  conv { ring, },
end

-- norm_num examples:
example : 22 + 7 * 4 + 3 * 8 = 74 :=
begin
  conv { norm_num, },
end

example (x : ℕ) : 22 + 7 * x + 3 * 8 = 7 * x + 46 :=
begin
  conv { norm_num, },
end