Theorems · Theorem · order theory
le_neg
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LE α] [AddLeftMono α] [AddRightMono α] {a b : α}, a ≤ -b ↔ b ≤ -a- Defined in
- Mathlib.Algebra.Order.Group.OrderIso
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- AddRightMonostatement and proof · cited by 367
- OrderIso.negproof · cited by 27
- OrderIso.le_symm_applyproof · cited by 14
Cited by16
Results whose statement or proof uses this declaration.
- Real.arcsin_negproof · cited by 11
- Set.neg_Iciproof · cited by 6
- LaurentSeries.valuation_le_iff_coeff_lt_eq_zeroproof · cited by 3
- le_div_iff_of_negproof · cited by 3
- Int.floor_negproof · cited by 3
- ZLattice.exists_finsetSum_norm_rpow_le_tsumproof · cited by 2
- MeasureTheory.Martingale.bddAbove_range_iff_bddBelow_rangeproof · cited by 2
- ODE_solution_unique_of_mem_Icc_leftproof · cited by 2
- le_neg_of_le_negproof · cited by 2
- PythagoreanTriple.isPrimitiveClassified_of_coprimeproof · cited by 2
- le_abs'proof · cited by 1
- ENNReal.exists_frequently_lt_of_liminf_ne_top'proof · cited by 1