Theorems · Definition · ring theory

StarAlgEquiv.trans

{R : Type u_2} →
  {A : Type u_3} →
    {B : Type u_4} →
      {C : Type u_5} →
        [inst : Add A] →
          [inst_1 : Add B] →
            [inst_2 : Mul A] →
              [inst_3 : Mul B] →
                [inst_4 : SMul R A] →
                  [inst_5 : SMul R B] →
                    [inst_6 : Star A] →
                      [inst_7 : Star B] →
                        [inst_8 : Add C] →
                          [inst_9 : Mul C] →
                            [inst_10 : SMul R C] → [inst_11 : Star C] → (A ≃⋆ₐ[R] B) → (B ≃⋆ₐ[R] C) → A ≃⋆ₐ[R] C

Transitivity of StarAlgEquiv.

Defined in

Mathlib.Algebra.Star.StarAlgHom

Cited by

11 results in Mathlib

Foundations

Depth 22 from the axioms · uses Quot.sound

Assumes

AddAddMulMulSMulSMulStarStarAddMulSMulStar