mul_mem — Mathlib

English

A submonoid is closed under multiplication: if x and y are in S, then xy is in S.

Русский

Подмономод замкнут по умножению: если x,y ∈ S, то xy ∈ S.

LaTeX

$$$$ x \\in S \\land y \\in S \\Rightarrow x y \\in S $$$$

Lean4

/-- A submonoid is closed under multiplication. -/
@[to_additive /-- An `AddSubmonoid` is closed under addition. -/
    ]
protected theorem mul_mem {x y : M} : x ∈ S → y ∈ S → x * y ∈ S :=
  mul_mem

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