Theorems · Theorem · order theory
Left.neg_pos_iff
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LT α] [AddLeftStrictMono α] {a : α}, 0 < -a ↔ a < 0Uses left co(ntra)variant.
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- AddGroupLTAddLeftStrictMono
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
- add_zeroproof · cited by 2,707
- add_neg_cancelproof · cited by 213
- AddLeftStrictMonostatement and proof · cited by 203
- add_lt_add_iff_leftproof · cited by 30
Cited by22
Results whose statement or proof uses this declaration.
- neg_posproof · cited by 74
- abs_posproof · cited by 45
- neg_pos_of_negproof · cited by 13
- IsAddIndecomposable.mem_or_neg_mem_closure_baseOfproof · cited by 5
- Real.binEntropy_neg_of_negproof · cited by 4
- Complex.arg_neg_coe_angleproof · cited by 3
- Complex.arg_neg_eq_arg_add_pi_of_im_negproof · cited by 3
- Real.contDiffAt_logproof · cited by 3
- sameRay_or_sameRay_neg_iff_not_linearIndependentproof · cited by 2
- ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc_of_integral_eq_zeroproof · cited by 1
- integral_log_from_zeroproof · cited by 1
- not_isAddCyclic_of_denselyOrderedproof · cited by 1