Theorems · Theorem · group theory
AddCon.neg
∀ {M : Type u_1} [inst : AddGroup M] (c : AddCon M) {x y : M}, c x y → c (-x) (-y)Additive congruence relations preserve negation.
- Defined in
- Mathlib.GroupTheory.Congruence.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddGroupstatement and proof · cited by 4,410
- neg_add_cancelproof · cited by 256
- AddConstatement and proof · cited by 138
- AddCon.reflproof · cited by 6
- AddCon.map_of_add_left_rel_zeroproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- AddCon.zsmulproof · cited by 1
- RingCon.negproof · cited by 1
- AddCon.subproof · cited by 1