Theorems · Theorem · group theory
AddCon.add
∀ {M : Type u_1} [inst : Add M] (c : AddCon M) {w x y z : M}, c w x → c y z → c (w + y) (x + z)Additive congruence relations preserve addition.
- Defined in
- Mathlib.GroupTheory.Congruence.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- Add
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- AddConstatement and proof · cited by 138
- AddCon.add'proof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- AddLocalization.mk_eq_addMonoidOf_mk'_applyproof · cited by 3
- AddCon.list_sumproof · cited by 2
- AddCon.addConGen_eqproof · cited by 1
- AddLocalization.r_eq_r'proof · cited by 1
- AddCon.subproof · cited by 1
- SymmetricPower.smulproof · cited by 0
- AddCon.vaddproof · cited by 0
- QuotientAddGroup.con_addSubgroupproof · cited by 0