Theorems · Theorem · commutative algebra
RingCon.mul
∀ {R : Type u_1} [inst : Add R] [inst_1 : Mul R] (c : RingCon R) {w x y z : R}, c w x → c y z → c (w * y) (x * z)- Defined in
- Mathlib.RingTheory.Congruence.Defs
- Cited by
- 8 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.
Cites4
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.toConproof · cited by 36
- Con.mul'proof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- TwoSidedIdeal.mul_mem_leftproof · cited by 8
- TwoSidedIdeal.mul_mem_rightproof · cited by 7
- RingCon.ringConGen_eqproof · cited by 2
- RingCon.mapGen_eq_map_of_surjectiveproof · cited by 1
- RingCon.coe_ofMatrix_eq_relationMapproof · cited by 1
- RingCon.ofMatrix_rel'proof · cited by 0
- RingCon.matrix_ofMatrixproof · cited by 0
- RingQuot.eqvGen_rel_eqproof · cited by 0