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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: 18536License: APACHE
import tactic.ring data.real.basic example (x y : ℕ) : x + y = y + x := by ring example (x y : ℕ) : x + y + y = 2 * y + x := by ring example (x y : ℕ) : x + id y = y + id x := by ring! example {α} [comm_ring α] (x y : α) : x + y + y - x = 2 * y := by ring example (x y : ℚ) : x / 2 + x / 2 = x := by ring example (x y : ℚ) : (x + y) ^ 3 = x ^ 3 + y ^ 3 + 3 * (x * y ^ 2 + x ^ 2 * y) := by ring example (x y : ℝ) : (x + y) ^ 3 = x ^ 3 + y ^ 3 + 3 * (x * y ^ 2 + x ^ 2 * y) := by ring example {α} [comm_semiring α] (x : α) : (x + 1) ^ 6 = (1 + x) ^ 6 := by try_for 15000 {ring} example (a n s: ℕ) : a * (n - s) = (n - s) * a := by ring example (x y z : ℚ) (hx : x ≠ 0) (hy : y ≠ 0) (hz : z ≠ 0) : x / (y / z) + y ⁻¹ + 1 / (y * -x) = -1/ (x * y) + (x * z + 1) / y := begin field_simp [hx, hy, hz], ring end example (a b c d x y : ℚ) (hx : x ≠ 0) (hy : y ≠ 0) : a + b / x + c / x^2 + d / x^3 = a + x⁻¹ * (y * b / y + (d / x + c) / x) := begin field_simp [hx, hy], ring end