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Theorems · Theorem · order theory

nonpos_of_neg_nonneg

∀ {α : Type u} [inst : AddGroup α] [inst_1 : LE α] [AddLeftMono α] {a : α}, 0 ≤ -a → a ≤ 0

Alias of the forward direction of Left.nonneg_neg_iff. Uses left co(ntra)variant.

Defined in
Mathlib.Algebra.Order.Group.Unbundled.Basic
Cited by
3 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext
Assumes
AddGroupLEAddLeftMono
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

selfZPow_mul_neg · cited by 3selfZPow_mul_negPolynomial.zero_lt_negOnePow_mul_eval_of_lt_roots_of_leadingCoeff_nonneg · cited by 2Polynomial.zero_lt_negOne…IsRealClosed.nonneg_iff_isSquare · cited by 1IsRealClosed.nonneg_iff_i…AddGroup · cited by 4410AddGroupAddLeftMono · cited by 687AddLeftMonoLeft.nonneg_neg_iff · cited by 14Left.nonneg_neg_iffnonpos_of_neg_nonnegCITED BYCITES

Cites3

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Cited by3

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