Theorems · Theorem · order theory
add_le_add_add_tsub
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : AddCommSemigroup α] [inst_2 : Sub α] [OrderedSub α] {a b c : α}
[AddLeftMono α], a + b ≤ a + c + (b - c)- Defined in
- Mathlib.Algebra.Order.Sub.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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_reflproof · cited by 2,061
- add_assocproof · cited by 746
- AddLeftMonostatement and proof · cited by 687
- add_le_addproof · cited by 666
- le_imp_le_of_le_of_leproof · cited by 576
- OrderedSubstatement and proof · cited by 236
- AddCommSemigroupstatement and proof · cited by 178
- le_add_tsubproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- le_tsub_add_addproof · cited by 0