Theorems · Theorem · order theory
AddLECancellable.lt_tsub_of_add_lt_left
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : AddCommSemigroup α] [inst_2 : Sub α] [OrderedSub α] {a b c : α},
AddLECancellable a → a + c < b → c < b - a- Defined in
- Mathlib.Algebra.Order.Sub.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- OrderedSubstatement and proof · cited by 236
- AddCommSemigroupstatement and proof · cited by 178
- AddLECancellablestatement and proof · cited by 87
- AddLECancellable.lt_tsub_of_add_lt_rightproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- AddLECancellable.lt_tsub_iff_leftproof · cited by 1
- AddLECancellable.tsub_lt_tsub_right_of_leproof · cited by 1
- lt_tsub_of_add_lt_leftproof · cited by 0