toIsCancelMul — Mathlib

English

From UniqueProds of G one obtains IsCancelMul G (left and right cancellation).

Русский

Из UniqueProds G следует IsCancelMul G (правое и левоеCancel).

LaTeX

$$$ \\forall G\\,[\\mathrm{UniqueProds }G] \\Rightarrow \\mathrm{IsCancelMul }G.$$$

Lean4

@[to_additive]
theorem toIsCancelMul [UniqueProds G] : IsCancelMul G
    where
  mul_left_cancel := toIsLeftCancelMul.mul_left_cancel
  mul_right_cancel _ _ _ h := op_injective <| toIsLeftCancelMul.mul_left_cancel _ <| unop_injective h

Похожие утверждения