Theorems · Definition · order theory

OrderMonoidIso.trans

{α : Type u_2} →
  {β : Type u_3} →
    {γ : Type u_4} →
      [inst : Preorder α] →
        [inst_1 : Preorder β] →
          [inst_2 : Preorder γ] →
            [inst_3 : Mul α] → [inst_4 : Mul β] → [inst_5 : Mul γ] → (α ≃*o β) → (β ≃*o γ) → α ≃*o γ

Transitivity of multiplication-preserving order isomorphisms

Defined in

Mathlib.Algebra.Order.Hom.Monoid

Cited by

11 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Quot.sound

Assumes

PreorderPreorderPreorderMulMulMul