Theorems · Theorem · real analysis
ENNReal.toReal_le_toReal
∀ {a b : ENNReal}, a ≠ ⊤ → b ≠ ⊤ → (a.toReal ≤ b.toReal ↔ a ≤ b)- Defined in
- Mathlib.Data.ENNReal.Real
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- NNRealproof · cited by 4,310
- ENNReal.ofNNRealproof · cited by 1,279
- ENNReal.toRealstatement and proof · cited by 859
Cited by17
Results whose statement or proof uses this declaration.
- ENNReal.toReal_monoproof · cited by 59
- MeasureTheory.eLpNorm_add_leproof · cited by 10
- MeasureTheory.enorm_setToFun_leproof · cited by 4
- MeasureTheory.MemLp.condExpproof · cited by 3
- MeasureTheory.measure_le_setLAverage_posproof · cited by 2
- MeasureTheory.VectorMeasure.norm_measure_le_variationproof · cited by 2
- MeasureTheory.measure_setLAverage_le_posproof · cited by 2
- ProbabilityTheory.IndepFun.integral_bilin_comp_comp'proof · cited by 2
- dist_integral_mulExpNegMulSq_comp_leproof · cited by 1
- MeasureTheory.eLpNorm_condExpL2_leproof · cited by 1
- Real.dist_mulExpNegMulSq_le_distproof · cited by 1
- ProbabilityTheory.IndepFun.integrable_bilinproof · cited by 1