Theorems · Theorem · group theory
Con.mul
∀ {M : Type u_1} [inst : Mul M] (c : Con M) {w x y z : M}, c w x → c y z → c (w * y) (x * z)Multiplicative congruence relations preserve multiplication.
- Defined in
- Mathlib.GroupTheory.Congruence.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- Mul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.mul'proof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- Localization.mk_eq_monoidOf_mk'_applyproof · cited by 4
- Localization.r_eq_r'proof · cited by 3
- Con.list_prodproof · cited by 2
- Con.conGen_eqproof · cited by 1
- Con.smulproof · cited by 0
- Con.divproof · cited by 0
- QuotientGroup.con_subgroupproof · cited by 0