Theorems · Theorem · order theory
AddLECancellable.lt_tsub_of_add_lt_right
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : AddCommSemigroup α] [inst_2 : Sub α] [OrderedSub α] {a b c : α},
AddLECancellable c → a + c < b → a < b - c- Defined in
- Mathlib.Algebra.Order.Sub.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.not_geproof · cited by 305
- 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
- le_tsub_addproof · cited by 10
- AddLECancellable.le_tsub_of_add_le_rightproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- AddLECancellable.lt_tsub_of_add_lt_leftproof · cited by 3
- AddLECancellable.lt_tsub_iff_right_of_leproof · cited by 2
- lt_tsub_of_add_lt_rightproof · cited by 0
- AddLECancellable.lt_tsub_iff_rightproof · cited by 0