Theorems · Theorem · real analysis
ENNReal.HolderConjugate.toReal_iff
∀ {p q : ENNReal}, 1 < p.toReal → (p.toReal.HolderConjugate q.toReal ↔ p.HolderConjugate q)- Defined in
- Mathlib.Data.Real.ConjExponents
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- ENNReal.toRealstatement and proof · cited by 859
- zero_lt_oneproof · cited by 598
- LT.lt.transproof · cited by 370
- Real.HolderConjugatestatement · cited by 78
- ENNReal.one_ne_topproof · cited by 65
- ENNReal.toReal_monoproof · cited by 59
- ENNReal.HolderConjugatestatement and proof · cited by 39
- ENNReal.toReal_pos_iffproof · cited by 20
- ENNReal.HolderConjugate.posproof · cited by 3
- ENNReal.HolderConjugate.lt_top_iff_one_ltproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- ENNReal.HolderConjugate.toNNReal_iffproof · cited by 1
- ENNReal.HolderConjugate.toRealproof · cited by 1