Theorems · Theorem · order theory
AddLECancellable.add_tsub_cancel_right
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : AddCommSemigroup α] [inst_2 : Sub α] [OrderedSub α] {a b : α},
AddLECancellable b → a + b - b = a- Defined in
- Mathlib.Algebra.Order.Sub.Defs
- Cited by
- 9 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.tsub_eq_of_eq_addproof · cited by 11
Cited by9
Results whose statement or proof uses this declaration.
- add_tsub_cancel_rightproof · cited by 172
- AddLECancellable.add_tsub_assoc_of_leproof · cited by 5
- Set.encard_sdiff_singleton_of_memproof · cited by 3
- AddLECancellable.lt_add_of_tsub_lt_rightproof · cited by 2
- AddLECancellable.lt_tsub_iff_right_of_leproof · cited by 2
- ENNReal.add_sub_cancel_rightproof · cited by 2
- AddLECancellable.add_add_tsub_cancelproof · cited by 1
- MeasureTheory.Measure.rnDeriv_self_addproof · cited by 1
- Set.encard_eq_add_one_iffproof · cited by 0