Theorems · Theorem · order theory

tsub_tsub_assoc

∀ {α : Type u_1} [inst : AddCommSemigroup α] [inst_1 : PartialOrder α] [ExistsAddOfLE α] [AddLeftMono α]
  [inst_4 : Sub α] [OrderedSub α] {a b c : α} [AddLeftReflectLE α], b ≤ a → c ≤ b → a - (b - c) = a - b + c

Defined in

Mathlib.Algebra.Order.Sub.Unbundled.Basic

Cited by

3 results in Mathlib

Foundations

Depth 12 from the axioms · uses propext, Quot.sound

Assumes

AddCommSemigroupPartialOrderExistsAddOfLEAddLeftMonoSubOrderedSubAddLeftReflectLE