Theorems · Theorem · group theory
Subsemigroup.closure_mono
∀ {M : Type u_1} [inst : Mul M] ⦃s t : Set M⦄, s ⊆ t → Subsemigroup.closure s ≤ Subsemigroup.closure tsubsemigroup closure of a set is monotone in its argument: if s ⊆ t,
then closure s ≤ closure t.
- Defined in
- Mathlib.Algebra.Group.Subsemigroup.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Mul
Around this declaration
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Subsemigroupstatement · cited by 323
- Set.Subset.transproof · cited by 218
- Subsemigroup.closurestatement · cited by 43
- Subsemigroup.subset_closureproof · cited by 16
- Subsemigroup.closure_leproof · cited by 13
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