Theorems · Theorem · order theory
AddLECancellable.le_tsub_of_add_le_left
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : AddCommSemigroup α] [inst_2 : Sub α] [OrderedSub α] {a b c : α},
AddLECancellable a → a + b ≤ c → b ≤ c - a- Defined in
- Mathlib.Algebra.Order.Sub.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 8 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.
- Preorderstatement and proof · cited by 7,952
- LE.le.transproof · cited by 3,151
- OrderedSubstatement and proof · cited by 236
- AddCommSemigroupstatement and proof · cited by 178
- AddLECancellablestatement and proof · cited by 87
- le_add_tsubproof · cited by 14
Cited by5
Results whose statement or proof uses this declaration.
- le_tsub_of_add_le_leftproof · cited by 11
- ENNReal.le_sub_of_add_le_leftproof · cited by 4
- AddLECancellable.le_tsub_of_add_le_rightproof · cited by 4
- ENat.le_sub_of_add_le_leftproof · cited by 3
- AddLECancellable.le_tsub_iff_leftproof · cited by 3