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Theorems · Theorem · group theory

AddCon.sub

∀ {M : Type u_1} [inst : AddGroup M] (c : AddCon M) {w x y z : M}, c w x → c y z → c (w - y) (x - z)

Additive congruence relations preserve subtraction.

Defined in
Mathlib.GroupTheory.Congruence.Defs
Cited by
1 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
Assumes
AddGroup
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Around this declaration

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

RingCon.sub · cited by 1RingCon.subDFunLike.coe · cited by 62936DFunLike.coeAddGroup · cited by 4410AddGroupsub_eq_add_neg · cited by 1023sub_eq_add_negAddCon · cited by 138AddConAddCon.add · cited by 8AddCon.addAddCon.neg · cited by 3AddCon.negAddCon.subCITED BYCITES

Cites6

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

Cited by1

Results whose statement or proof uses this declaration.