Theorems · Theorem · order theory
AddLECancellable.tsub_lt_tsub_left_of_le
∀ {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 - b) → b ≤ a → c < b → a - b < a - c- Cited by
- 2 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.
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
- LE.le.transproof · cited by 3,151
- 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
- tsub_le_tsub_leftproof · cited by 15
- AddLECancellable.tsub_inj_rightproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- AddLECancellable.tsub_lt_tsub_iff_left_of_le_of_leproof · cited by 1
- tsub_lt_tsub_left_of_leproof · cited by 0