Theorems · Theorem · order theory
AddLECancellable.eq_tsub_of_add_eq
∀ {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 - cSee AddLECancellable.eq_tsub_of_add_eq' for a version assuming that b = a + c itself is
cancellable rather than c.
- Defined in
- Mathlib.Algebra.Order.Sub.Defs
- Cited by
- 6 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.
Cites5
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
- 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 by6
Results whose statement or proof uses this declaration.
- eq_tsub_of_add_eqproof · cited by 11
- ENNReal.eq_sub_of_add_eqproof · cited by 6
- AddLECancellable.eq_tsub_iff_add_eq_of_leproof · cited by 3
- Set.encard_sdiffproof · cited by 2
- AddLECancellable.tsub_mulproof · cited by 2
- AddLECancellable.mul_tsubproof · cited by 1