Theorems · Theorem · order theory

AddLECancellable.le_tsub_iff_left

∀ {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}, AddLECancellable a → a ≤ c → (b ≤ c - a ↔ a + b ≤ c)

Defined in

Mathlib.Algebra.Order.Sub.Unbundled.Basic

Cited by

3 results in Mathlib

Foundations

Depth 10 from the axioms · uses propext, Quot.sound

Assumes

AddCommSemigroupPartialOrderExistsAddOfLEAddLeftMonoSubOrderedSub