Theorems · Theorem · order theory
neg_le_neg_iff
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LE α] [AddLeftMono α] {a b : α} [AddRightMono α], -a ≤ -b ↔ b ≤ a- Cited by
- 57 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- zero_addproof · cited by 2,366
- AddLeftMonostatement and proof · cited by 687
- AddRightMonostatement and proof · cited by 367
- add_neg_cancelproof · cited by 213
- neg_add_cancel_rightproof · cited by 75
- add_le_add_iff_rightproof · cited by 47
- add_le_add_iff_leftproof · cited by 45
Cited by58
Results whose statement or proof uses this declaration.
- neg_le_negproof · cited by 34
- OrderIso.negproof · cited by 27
- neg_convexOn_iffproof · cited by 10
- sub_le_sub_iff_leftproof · cited by 8
- MonotoneOn.negproof · cited by 8
- AntitoneOn.negproof · cited by 8
- norm_jacobiTheta₂_term_leproof · cited by 5
- ZMod.natAbs_valMinAbs_leproof · cited by 5
- max_neg_negproof · cited by 5
- padicNorm.dvd_iff_norm_leproof · cited by 5
- abs_le_max_abs_absproof · cited by 5
- IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_dvdproof · cited by 5