copy — Mathlib

English

If c is invertible and a b = c, then the inverse respects left multiplication: a c^{-1} = b implies a = c b.

Русский

Пусть c обратим; если a b = c, то a c^{-1} = b эквивалентно a = c b.

LaTeX

$$$\\forall a,b,c\\text{ with invertible } c,\\ a c^{-1} = b \\iff a = c b$$$

Lean4

/-- If `r` is invertible and `s = r`, then `s` is invertible. -/
abbrev copy [MulOneClass α] {r : α} (hr : Invertible r) (s : α) (hs : s = r) : Invertible s :=
  hr.copy' _ _ hs rfl

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