Theorems · Theorem · group theory
AddCon.eq
∀ {M : Type u_1} [inst : Add M] (c : AddCon M) {a b : M}, ↑a = ↑b ↔ c a bTwo elements are related by an additive congruence relation c iff
they are represented by the same element of the quotient by c.
- Defined in
- Mathlib.GroupTheory.Congruence.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
- Assumes
- Add
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.Quotientstatement · cited by 54
- Quotient.eq''proof · cited by 44
- AddCon.toQuotientstatement · cited by 38
Cited by9
Results whose statement or proof uses this declaration.
- Module.DirectLimit.of_fproof · cited by 3
- AddCon.kerLift_injectiveproof · cited by 1
- AddMonoid.Coprod.mk_eq_mkproof · cited by 1
- AddCon.map_of_add_left_rel_zeroproof · cited by 1
- AddCon.mk'_kerproof · cited by 1
- AddCon.induction_on_addUnitsstatement and proof · cited by 0
- AddCon.liftOnAddUnits_mkstatement · cited by 0
- AddCon.comap_eqproof · cited by 0
- AddCon.map_applystatement · cited by 0