Theorems · Theorem · group theory
Submonoid.op_closure
∀ {M : Type u_2} [inst : MulOneClass M] (s : Set M),
(Submonoid.closure s).op = Submonoid.closure (MulOpposite.unop ⁻¹' s)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Submonoidstatement and proof · cited by 3,086
- MulOppositestatement and proof · cited by 1,135
- MulOneClassstatement and proof · cited by 1,018
- InfSet.sInfproof · cited by 935
- MulOpposite.opproof · cited by 520
- MulOpposite.unopstatement and proof · cited by 268
- Function.Surjective.forallproof · cited by 214
- Submonoid.closurestatement · cited by 167
Cited by2
Results whose statement or proof uses this declaration.
- Submonoid.closure_induction_rightproof · cited by 2
- Submonoid.unop_closureproof · cited by 0