instFaithfulSMul — Mathlib

English

If M acts on α and the action is faithful, then Units M also acts faithfully on α.

Русский

Если M действует на α, и действиеFaithful, то и Units M действуетFaithfully на α.

LaTeX

$$$ \\operatorname{FaithfulSMul} (M) (\\alpha) \\Rightarrow \\operatorname{FaithfulSMul} (Units M) (\\alpha)$$$

Lean4

@[to_additive]
instance [Monoid M] [SMul M α] [FaithfulSMul M α] : FaithfulSMul Mˣ α where
  eq_of_smul_eq_smul h := Units.ext <| eq_of_smul_eq_smul h

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