Theorems · Theorem · order theory
neg_add_le_iff_le_add
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LE α] [AddLeftMono α] {a b c : α}, -b + a ≤ c ↔ a ≤ b + c- Cited by
- 6 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- AddGroupLEAddLeftMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddLeftMonostatement and proof · cited by 687
- add_neg_cancel_leftproof · cited by 76
- add_le_add_iff_leftproof · cited by 45
Cited by6
Results whose statement or proof uses this declaration.
- le_add_ciInfproof · cited by 2
- neg_add_le_iff_le_add'proof · cited by 1
- neg_add_le_of_le_addproof · cited by 0
- neg_add_nonpos_iffproof · cited by 0
- add_neg_le_iff_le_add'proof · cited by 0
- Finset.sum_Icc_succ_eq_add_endpointsproof · cited by 0