Theorems · Definition · commutative algebra

ModuleCon.mk.noConfusion

{S : Type u_2} →
  {M : Type u_3} →
    {inst : Add M} →
      {inst_1 : SMul S M} →
        {P : Sort u} →
          {toAddCon : AddCon M} →
            {smul : ∀ (s : S) {x y : M}, toAddCon.toSetoid x y → toAddCon.toSetoid (s • x) (s • y)} →
              {toAddCon' : AddCon M} →
                {smul' : ∀ (s : S) {x y : M}, toAddCon'.toSetoid x y → toAddCon'.toSetoid (s • x) (s • y)} →
                  { toAddCon := toAddCon, smul := smul } = { toAddCon := toAddCon', smul := smul' } →
                    (toAddCon ≍ toAddCon' → P) → P

Defined in: Mathlib.Algebra.Module.Congruence.Defs
Cited by: 1 results in Mathlib
Foundations: Depth 9 from the axioms · uses no axioms

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AddConstatement and proof · cited by 138
AddCon.toSetoidstatement · cited by 20
ModuleConstatement · cited by 4
ModuleCon.noConfusionproof · cited by 0

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ModuleCon.mk.injproof · cited by 1