instLeftCancelSemigroup — Mathlib

English

If M is a LeftCancelSemigroup, then Germ l M is a LeftCancelSemigroup; i.e., left cancellation holds for germs.

Русский

Если M — левыйCancelSemigroup, то Germ l M — левыйCancelSemigroup; т.е. левое отменение выполняется для жерм.

LaTeX

$$$ [\\text{LeftCancelSemigroup } M] \\Rightarrow [\\text{LeftCancelSemigroup } (\\mathrm{Germ}(l, M))]$$$

Lean4

@[to_additive]
instance instLeftCancelSemigroup [LeftCancelSemigroup M] : LeftCancelSemigroup (Germ l M) where
  mul_left_cancel _ _ _ := mul_left_cancel

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