Theorems · Definition · ring theory

BialgEquiv.casesOn

{R : Type u} →
  [inst : CommSemiring R] →
    {A : Type v} →
      {B : Type w} →
        [inst_1 : Semiring A] →
          [inst_2 : Semiring B] →
            [inst_3 : Algebra R A] →
              [inst_4 : Algebra R B] →
                [inst_5 : CoalgebraStruct R A] →
                  [inst_6 : CoalgebraStruct R B] →
                    {motive : (A ≃ₐc[R] B) → Sort u_1} →
                      (t : A ≃ₐc[R] B) →
                        ((toCoalgEquiv : A ≃ₗc[R] B) →
                            (map_mul' :
                                ∀ (x y : A), toCoalgEquiv.toFun (x * y) = toCoalgEquiv.toFun x * toCoalgEquiv.toFun y) →
                              motive { toCoalgEquiv := toCoalgEquiv, map_mul' := map_mul' }) →
                          motive t

Defined in

Mathlib.RingTheory.Bialgebra.Equiv

Cited by

0 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebraCoalgebraStructCoalgebraStruct