Theorems · Theorem · order theory
neg_le_sub_iff_le_add
∀ {α : Type u} [inst : AddCommGroup α] [inst_1 : LE α] [AddLeftMono α] {a b c : α}, -b ≤ a - c ↔ c ≤ a + b- Cited by
- 4 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommGroupLEAddLeftMono
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.
- AddCommGroupstatement and proof · cited by 12,871
- AddLeftMonostatement and proof · cited by 687
- le_sub_iff_add_leproof · cited by 41
- neg_add_le_iff_le_add'proof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- abs_sub_le_iffproof · cited by 34
- wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonnegproof · cited by 2
- Set.mem_Icc_iff_abs_leproof · cited by 1
- neg_le_sub_iff_le_add'proof · cited by 1