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Theorems · Definition · group theory

Con.unop

{M : Type u_1} → [inst : Mul M] → Con Mᵐᵒᵖ → Con M

If c is a multiplicative congruence on Mᵐᵒᵖ, then (a, b) ↦ c bᵒᵖ aᵒᵖ is a multiplicative congruence on M.

Defined in
Mathlib.GroupTheory.Congruence.Opposite
Cited by
1 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
Mul
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Around this declaration

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

RingCon.unop · cited by 3RingCon.unopCon.orderIsoOp · cited by 2Con.orderIsoOpCon.orderIsoOp_symm_apply · cited by 0Con.orderIsoOp_symm_applyDFunLike.coe · cited by 62936DFunLike.coeMulOpposite · cited by 1135MulOppositeMulOpposite.op · cited by 520MulOpposite.opCon · cited by 152ConCon.unopCITED BYCITES

Cites4

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Cited by3

Results whose statement or proof uses this declaration.