Mathlib Map

Theorems · Theorem · commutative algebra

ModuleCon.mk.inj

∀ {S : Type u_2} {M : Type u_3} {inst : Add M} {inst_1 : SMul S M} {toAddCon : AddCon M}
  {smul : ∀ (s : S) {x y : M}, toAddCon.toSetoid x y → toAddCon.toSetoid (s • x) (s • y)} {toAddCon_1 : AddCon M}
  {smul_1 : ∀ (s : S) {x y : M}, toAddCon_1.toSetoid x y → toAddCon_1.toSetoid (s • x) (s • y)},
  { toAddCon := toAddCon, smul := smul } = { toAddCon := toAddCon_1, smul := smul_1 } → toAddCon = toAddCon_1
Defined in
Mathlib.Algebra.Module.Congruence.Defs
Cited by
1 results in Mathlib
Foundations
Depth 10 from the axioms · uses no axioms
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ModuleCon.mk.injEq · cited by 0mk.injEqAddCon · cited by 138AddConAddCon.toSetoid · cited by 20AddCon.toSetoidModuleCon · cited by 4ModuleConModuleCon.mk.noConfusion · cited by 1mk.noConfusionmk.injCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.