principal_swap_iff — Mathlib

English

Principal op swapped is equivalent to Principal op: Principal(Function.swap(op)) o iff Principal op o.

Русский

Principal(op) и Principal(Function.swap(op)) эквивалентны: Principal(Function.swap(op)) o ⇔ Principal op o.

LaTeX

$$$$ \operatorname{Principal}(\mathrm{Function.swap}(op))\ o \ \leftrightarrow \ \operatorname{Principal}(op)\ o. $$$$

Lean4

theorem principal_swap_iff : Principal (Function.swap op) o ↔ Principal op o := by
  constructor <;> exact fun h a b ha hb => h hb ha

Похожие утверждения