Theorems · Theorem · commutative algebra
RingCon.eq
∀ {R : Type u_1} [inst : Add R] [inst_1 : Mul R] (c : RingCon R) {a b : R}, ↑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.RingTheory.Congruence.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
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
- RingConstatement and proof · cited by 219
- RingCon.Quotientstatement · cited by 118
- RingCon.toQuotientstatement · cited by 69
- Quotient.eq''proof · cited by 44
Cited by2
Results whose statement or proof uses this declaration.
- RingCon.factorₐ_applystatement · cited by 0
- RingCon.map_applystatement · cited by 0