Theorems · Theorem · order theory
AddLECancellable.tsub_lt_tsub_iff_left_of_le
∀ {α : Type u_1} [inst : AddCommMonoid α] [inst_1 : LinearOrder α] [CanonicallyOrderedAdd α] [inst_3 : Sub α]
[OrderedSub α] {a b c : α}, AddLECancellable a → AddLECancellable b → b ≤ a → (a - b < a - c ↔ c < b)See lt_tsub_iff_left_of_le_of_le for a weaker statement in a partial order.
- Defined in
- Mathlib.Algebra.Order.Sub.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- LinearOrderstatement and proof · cited by 8,572
- OrderedSubstatement and proof · cited by 236
- CanonicallyOrderedAddstatement and proof · cited by 229
- AddLECancellablestatement and proof · cited by 87
- lt_iff_lt_of_le_iff_leproof · cited by 54
- AddLECancellable.tsub_le_tsub_iff_leftproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- tsub_lt_tsub_iff_left_of_leproof · cited by 4