Theorems · Theorem · group theory
Submonoid.mul_mem_units
∀ {M : Type u_1} [inst : Monoid M] (S : Submonoid M) {x y : Mˣ}, x ∈ S.units → y ∈ S.units → x * y ∈ S.units- Defined in
- Mathlib.Algebra.Group.Submonoid.Units
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext
- Assumes
- Monoid
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Subgroupstatement · cited by 3,593
- Submonoidstatement and proof · cited by 3,086
- Unitsstatement and proof · cited by 2,804
- MulMemClass.mul_memproof · cited by 173
- Submonoid.unitsstatement and proof · cited by 40
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