Theorems · Theorem · functional analysis
RCLike.ofReal_mul_pos_iff
∀ {K : Type u_1} [inst : RCLike K] (x : ℝ) (z : K), 0 < ↑x * z ↔ x < 0 ∧ z < 0 ∨ 0 < x ∧ 0 < z- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RCLikestatement and proof · cited by 2,829
- MulZeroClass.zero_mulproof · cited by 1,625
- LT.lt.ne'proof · cited by 1,417
- LT.lt.neproof · cited by 872
- RCLike.ofRealstatement and proof · cited by 350
- RCLike.reproof · cited by 319
- lt_trichotomyproof · cited by 178
- RCLike.improof · cited by 161
- RCLike.toPartialOrderstatement · cited by 106
- not_lt_of_gtproof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- RCLike.ofReal_mul_neg_iffproof · cited by 0