Theorems · Theorem · group theory
Subsemigroup.op_closure
∀ {M : Type u_2} [inst : Mul M] (s : Set M), (Subsemigroup.closure s).op = Subsemigroup.closure (MulOpposite.unop ⁻¹' s)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Mul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Set.preimagestatement and proof · cited by 4,946
- MulOppositestatement and proof · cited by 1,135
- InfSet.sInfproof · cited by 935
- MulOpposite.opproof · cited by 520
- Subsemigroupstatement and proof · cited by 323
- MulOpposite.unopstatement and proof · cited by 268
- Function.Surjective.forallproof · cited by 214
- InfSetproof · cited by 145
- Subsemigroup.closurestatement · cited by 43
Cited by1
Results whose statement or proof uses this declaration.
- Subsemigroup.unop_closureproof · cited by 0