Theorems · Theorem · order theory
le_add_tsub
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : AddCommSemigroup α] [inst_2 : Sub α] [OrderedSub α] {a b : α},
a ≤ b + (a - b)- Defined in
- Mathlib.Algebra.Order.Sub.Defs
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 7 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.
- Preorderstatement and proof · cited by 7,952
- le_rflproof · cited by 1,558
- OrderedSubstatement and proof · cited by 236
- AddCommSemigroupstatement and proof · cited by 178
- tsub_le_iff_leftproof · cited by 38
Cited by14
Results whose statement or proof uses this declaration.
- add_tsub_cancel_of_leproof · cited by 79
- MeasureTheory.lintegral_add_leftproof · cited by 21
- tsub_le_tsub_rightproof · cited by 16
- tsub_le_tsub_leftproof · cited by 15
- AddLECancellable.le_tsub_of_add_le_leftproof · cited by 5
- add_tsub_le_assocproof · cited by 3
- AddLECancellable.le_add_tsub_swapproof · cited by 2
- add_tsub_add_le_tsub_rightproof · cited by 1
- tsub_tsub_le_tsub_addproof · cited by 1
- add_le_add_add_tsubproof · cited by 1
- tsub_le_tsub_add_tsubproof · cited by 0
- add_tsub_add_le_tsub_leftproof · cited by 0