Theorems · Theorem · order theory
AddLECancellable.tsub_lt_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 b → b ≤ a → (a - b < c ↔ a < b + c)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- LT.lt.leproof · cited by 2,189
- LT.lt.ne'proof · cited by 1,417
- AddLeftMonostatement and proof · cited by 687
- ExistsAddOfLEstatement and proof · cited by 330
- OrderedSubstatement and proof · cited by 236
- AddCommSemigroupstatement and proof · cited by 178
- LE.le.lt_of_neproof · cited by 116
- AddLECancellablestatement and proof · cited by 87
- add_tsub_cancel_of_leproof · cited by 79
- tsub_le_iff_leftproof · cited by 38
- AddLECancellable.lt_add_of_tsub_lt_leftproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- AddLECancellable.tsub_lt_iff_rightproof · cited by 4
- tsub_lt_iff_leftproof · cited by 2
- AddLECancellable.tsub_lt_iff_tsub_ltproof · cited by 1
- ENNReal.sub_lt_iff_lt_leftproof · cited by 0