Theorems · Theorem · order theory
AddLECancellable.tsub_le_tsub_iff_left
∀ {α : Type u_1} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [CanonicallyOrderedAdd α] [inst_3 : Sub α]
[OrderedSub α] {a b c : α}, AddLECancellable a → AddLECancellable c → c ≤ a → (a - b ≤ a - c ↔ c ≤ b)- Defined in
- Mathlib.Algebra.Order.Sub.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- PartialOrderstatement and proof · cited by 6,410
- LE.le.transproof · cited by 3,151
- add_commproof · cited by 1,535
- OrderedSubstatement and proof · cited by 236
- CanonicallyOrderedAddstatement and proof · cited by 229
- AddLECancellablestatement and proof · cited by 87
- le_add_selfproof · cited by 51
- tsub_le_iff_leftproof · cited by 38
- tsub_le_tsub_leftproof · cited by 15
- AddLECancellable.add_tsub_assoc_of_leproof · cited by 5
- AddLECancellable.le_tsub_iff_rightproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- ENNReal.sub_le_sub_iff_leftproof · cited by 3
- tsub_le_tsub_iff_leftproof · cited by 2
- AddLECancellable.tsub_right_injproof · cited by 2
- AddLECancellable.tsub_lt_tsub_iff_left_of_leproof · cited by 1