Theorems · Theorem · commutative algebra
RingCon.trans
∀ {R : Type u_1} [inst : Add R] [inst_1 : Mul R] (c : RingCon R) {x y z : R}, c x y → c y z → c x z- Defined in
- Mathlib.RingTheory.Congruence.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
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
- Con.toSetoidproof · cited by 38
- RingCon.toConproof · cited by 36
- Setoid.trans'proof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- RingCon.ringConGen_eqproof · cited by 2
- RingQuot.eqvGen_rel_eqproof · cited by 0
- RingCon.mapGen_apply_apply_of_surjectiveproof · cited by 0