Theorems · Theorem · order theory
AddLECancellable.le_tsub_iff_right
∀ {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 ↔ b + a ≤ c)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- add_commproof · cited by 1,535
- AddLeftMonostatement and proof · cited by 687
- ExistsAddOfLEstatement and proof · cited by 330
- OrderedSubstatement and proof · cited by 236
- AddCommSemigroupstatement and proof · cited by 178
- AddLECancellablestatement and proof · cited by 87
- AddLECancellable.le_tsub_iff_leftproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- le_tsub_iff_rightproof · cited by 5
- AddLECancellable.tsub_le_tsub_iff_leftproof · cited by 4
- AddLECancellable.le_tsub_iff_le_tsubproof · cited by 1