Theorems · Theorem · order theory

OrderRingHom.cancel_left

∀ {α : Type u_2} {β : Type u_3} {γ : Type u_4} [inst : NonAssocSemiring α] [inst_1 : Preorder α]
  [inst_2 : NonAssocSemiring β] [inst_3 : Preorder β] [inst_4 : NonAssocSemiring γ] [inst_5 : Preorder γ] {f : β →+*o γ}
  {g₁ g₂ : α →+*o β}, Function.Injective ⇑f → (f.comp g₁ = f.comp g₂ ↔ g₁ = g₂)

Defined in

Mathlib.Algebra.Order.Hom.Ring

Cited by

0 results in Mathlib

Foundations

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

Assumes

NonAssocSemiringPreorderNonAssocSemiringPreorderNonAssocSemiringPreorder