Theorems · Theorem · order theory
AddLECancellable.lt_of_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} [AddLeftReflectLT α], AddLECancellable b → c ≤ a → a - b < a - c → c < b- Cited by
- 2 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.
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
- AddLeftMonostatement and proof · cited by 687
- ExistsAddOfLEstatement and proof · cited by 330
- OrderedSubstatement and proof · cited by 236
- AddCommSemigroupstatement and proof · cited by 178
- tsub_add_cancel_of_leproof · cited by 112
- AddLECancellablestatement and proof · cited by 87
- AddLeftReflectLTstatement and proof · cited by 33
- lt_of_add_lt_add_leftproof · cited by 9
- AddLECancellable.lt_add_of_tsub_lt_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
- lt_of_tsub_lt_tsub_left_of_leproof · cited by 0