mkQ_surjective — Mathlib

English

If S is a monoid acting on R, and M is an R-module, then the quotient M/P supports a DistribMulAction of S given by a • [x] = [a • x].

Русский

Если S — моноид, действующий на R, и M — R-модуль, то на M/P действует DistribMulAction через a • [x] = [a • x].

LaTeX

$$$\forall a \in S,\forall [x] \in M/P,\ a \cdot [x] = [a \cdot x]$$$

Lean4

theorem mkQ_surjective : Function.Surjective p.mkQ := by rintro ⟨x⟩; exact ⟨x, rfl⟩

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