Theorems · Theorem · order theory
add_neg_le_iff_le_add
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LE α] [AddRightMono α] {a b c : α}, a + -b ≤ c ↔ a ≤ c + b- Cited by
- 6 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- AddGroupLEAddRightMono
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
- AddRightMonostatement and proof · cited by 367
- neg_add_cancel_rightproof · cited by 75
- add_le_add_iff_rightproof · cited by 47
Cited by6
Results whose statement or proof uses this declaration.
- le_ciInf_addproof · cited by 2
- abs_abs_sub_abs_leproof · cited by 1
- add_neg_nonpos_iffproof · cited by 0
- add_neg_nonpos_iff_leproof · cited by 0
- Finset.sum_Icc_of_even_eq_rangeproof · cited by 0
- Finset.sum_Icc_succ_eq_add_endpointsproof · cited by 0