ext — Mathlib

English

If two congruences have the same binary relation, they are equal.

Русский

Если две конгруэнции имеют одинаковую бинарную relation, они равны.

LaTeX

$$$\\forall x,y,\\; c x y \\Leftrightarrow d x y \\Rightarrow c = d$$$

Lean4

/-- Extensionality rule for congruence relations. -/
@[to_additive (attr := ext) /-- Extensionality rule for additive congruence relations. -/
    ]
theorem ext {c d : Con M} (H : ∀ x y, c x y ↔ d x y) : c = d :=
  ext' <| by ext; apply H

Похожие утверждения