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Theorems · Theorem · logic and foundations

Hyperreal.infinitePos_neg

Deprecated since 2026-01-05Mathlib marks this declaration as deprecated.

∀ {x : ℝ*}, (-x).InfinitePos ↔ x.InfiniteNeg
Defined in
Mathlib.Analysis.Real.Hyperreal
Cited by
6 results in Mathlib
Foundations
Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Hyperreal.infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos · cited by 3Hyperreal.infiniteNeg_mul…Hyperreal.infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg · cited by 3Hyperreal.infiniteNeg_mul…Hyperreal.infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg · cited by 3Hyperreal.infinitePos_mul…Hyperreal.infiniteNeg_add_not_infinitePos · cited by 3Hyperreal.infiniteNeg_add…Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg · cited by 3Hyperreal.infiniteNeg_iff…Hyperreal.infinite_neg · cited by 2Hyperreal.infinite_negneg_neg · cited by 960neg_negHyperreal · cited by 172HyperrealHyperreal.InfinitePos · cited by 44Hyperreal.InfinitePosHyperreal.InfiniteNeg · cited by 38Hyperreal.InfiniteNegHyperreal.InfiniteNeg.neg · cited by 2InfiniteNeg.negHyperreal.InfinitePos.neg · cited by 2InfinitePos.negHyperreal.infinitePos_negCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by6

Results whose statement or proof uses this declaration.