Theorems · Theorem · logic and foundations
Hyperreal.infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos
Deprecated since 2026-01-05Mathlib marks this declaration as deprecated.
∀ {x y : ℝ*}, x.InfiniteNeg → ¬y.Infinitesimal → 0 < y → (x * y).InfiniteNeg- Defined in
- Mathlib.Analysis.Real.Hyperreal
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Hyperrealstatement and proof · cited by 172
- Hyperreal.InfinitePosproof · cited by 44
- Hyperreal.Infinitesimalstatement and proof · cited by 41
- Hyperreal.InfiniteNegstatement and proof · cited by 38
- neg_mul_eq_neg_mulproof · cited by 20
- Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_posproof · cited by 6
- Hyperreal.infinitePos_negproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Hyperreal.infinite_mul_of_infinite_not_infinitesimalproof · cited by 2
- Hyperreal.infiniteNeg_mul_infinitePosproof · cited by 0
- Hyperreal.infiniteNeg_mul_of_not_infinitesimal_pos_infiniteNegproof · cited by 0