Theorems · Theorem · group theory
Con.eq
∀ {M : Type u_1} [inst : Mul M] (c : Con M) {a b : M}, ↑a = ↑b ↔ c a bTwo elements are related by a 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
- Mul
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
- Constatement and proof · cited by 152
- Con.Quotientstatement · cited by 48
- Quotient.eq''proof · cited by 44
- Con.toQuotientstatement · cited by 33
Cited by9
Results whose statement or proof uses this declaration.
- Monoid.PushoutI.of_comp_eq_baseproof · cited by 3
- HNNExtension.t_mul_ofproof · cited by 2
- Con.mk'_kerproof · cited by 1
- Monoid.Coprod.mk_eq_mkproof · cited by 1
- Con.map_applystatement · cited by 0
- Con.kerLift_injectiveproof · cited by 0
- Con.comap_eqproof · cited by 0
- Con.induction_on_unitsstatement and proof · cited by 0
- Con.liftOnUnits_mkstatement · cited by 0