Mathlib Map

Theorems · Definition · group theory

Submonoid.equivOp

{M : Type u_2} → [inst : MulOneClass M] → (H : Submonoid M) → ↥H ≃ ↥H.op

Bijection between a submonoid H and its opposite.

Defined in
Mathlib.Algebra.Group.Submonoid.MulOpposite
Cited by
2 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Quot.sound
Assumes
MulOneClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Subsemiring.addEquivOp · cited by 8Subsemiring.addEquivOpSubmonoid.equivOp_apply_coe · cited by 0Submonoid.equivOp_apply_c…Submonoid.equivOp_symm_apply_coe · cited by 0Submonoid.equivOp_symm_ap…Equiv · cited by 8337EquivSubmonoid · cited by 3086SubmonoidMulOpposite · cited by 1135MulOppositeMulOneClass · cited by 1018MulOneClassSubmonoid.op · cited by 38Submonoid.opEquiv.subtypeEquiv · cited by 32Equiv.subtypeEquivMulOpposite.opEquiv · cited by 24MulOpposite.opEquivSubmonoid.equivOpCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.