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Theorems · Definition · group theory

AddSubmonoid.equivOp

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

Bijection between an additive 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
AddZeroClass
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Around this declaration

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

AddSubmonoid.equivOp_apply_coe · cited by 0AddSubmonoid.equivOp_appl…AddSubmonoid.equivOp_symm_apply_coe · cited by 0AddSubmonoid.equivOp_symm…Equiv · cited by 8337EquivAddZeroClass · cited by 1237AddZeroClassAddSubmonoid · cited by 1178AddSubmonoidAddOpposite · cited by 452AddOppositeEquiv.subtypeEquiv · cited by 32Equiv.subtypeEquivAddSubmonoid.op · cited by 28AddSubmonoid.opAddOpposite.opEquiv · cited by 20AddOpposite.opEquivAddSubmonoid.equivOpCITED BYCITES

Cites7

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

Cited by2

Results whose statement or proof uses this declaration.