Theorems · Theorem · group theory
Subsemigroup.closure_eq_of_le
∀ {M : Type u_1} [inst : Mul M] {s : Set M} {S : Subsemigroup M},
s ⊆ ↑S → S ≤ Subsemigroup.closure s → Subsemigroup.closure s = S- 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
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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
- SetLike.coestatement and proof · cited by 8,199
- le_antisymmproof · cited by 2,068
- Subsemigroupstatement and proof · cited by 323
- Subsemigroup.closurestatement and proof · cited by 43
- Subsemigroup.closure_leproof · cited by 13
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