Theorems · Theorem · order theory
neg_le
∀ {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
- 27 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.symm_apply_leproof · cited by 5
Cited by27
Results whose statement or proof uses this declaration.
- abs_leproof · cited by 64
- Real.arcsin_negproof · cited by 11
- Set.neg_Iicproof · cited by 8
- Real.abs_log_sub_add_sum_range_leproof · cited by 4
- Complex.arg_of_im_negproof · cited by 3
- SchwartzMap.isBigO_cocompact_rpowproof · cited by 3
- MeasureTheory.Martingale.bddAbove_range_iff_bddBelow_rangeproof · cited by 2
- Seminorm.abs_le_of_leproof · cited by 2
- Real.sin_nonpos_of_nonpos_of_neg_pi_leproof · cited by 2
- ODE_solution_unique_of_mem_Icc_leftproof · cited by 2
- ProbabilityTheory.rpow_abs_le_mul_max_exp_of_posproof · cited by 2
- bdd_le_mul_tendsto_zeroproof · cited by 1