Theorems · Theorem · order theory
AddLECancellable.add_tsub_assoc_of_le
∀ {α : Type u_1} [inst : AddCommSemigroup α] [inst_1 : PartialOrder α] [ExistsAddOfLE α] [AddLeftMono α]
[inst_4 : Sub α] [OrderedSub α] {b c : α}, AddLECancellable c → c ≤ b → ∀ (a : α), a + b - c = a + (b - c)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- add_assocproof · cited by 746
- 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
- add_tsub_cancel_of_leproof · cited by 79
- AddLECancellable.add_tsub_cancel_rightproof · cited by 9
Cited by5
Results whose statement or proof uses this declaration.
- add_tsub_assoc_of_leproof · cited by 16
- AddLECancellable.tsub_le_tsub_iff_leftproof · cited by 4
- AddLECancellable.tsub_add_eq_add_tsubproof · cited by 2
- AddLECancellable.tsub_add_tsub_commproof · cited by 1
- AddLECancellable.add_add_tsub_cancelproof · cited by 1