eq_one_of_mul_right — Mathlib

English

In a Left Cancel Monoid with subsingleton units, if a · b = 1, then a = 1.

Русский

В левоканонизированном моноиде сSubs единицами, если a·b = 1, то a = 1.

LaTeX

$$$ a \cdot b = 1 \Rightarrow a = 1 $$$

Lean4

@[to_additive]
protected theorem eq_one_of_mul_right (h : a * b = 1) : a = 1 :=
  congr_arg Units.inv <|
    Subsingleton.elim (Units.mk _ _ (by rw [← mul_left_cancel_iff (a := a), ← mul_assoc, h, one_mul, mul_one]) h) 1

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