Theorems · Theorem · real analysis
ENNReal.HolderTriple.inv_sub_inv_eq_inv
∀ (p q : ENNReal) {r : ENNReal} [p.HolderTriple q r], r ≠ 0 → r⁻¹ - q⁻¹ = p⁻¹- Defined in
- Mathlib.Data.ENNReal.Holder
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ENNReal.HolderTriple
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.
- ENNRealstatement and proof · cited by 9,879
- ne_of_ltproof · cited by 203
- pos_iff_ne_zeroproof · cited by 180
- ENNReal.HolderTriplestatement and proof · cited by 65
- ENNReal.HolderTriple.inv_eqproof · cited by 4
- ENNReal.sub_eq_of_eq_addproof · cited by 2
- ENNReal.HolderTriple.inv_le_invproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- ENNReal.HolderConjugate.one_sub_invproof · cited by 2
- ENNReal.HolderTriple.unique_of_ne_zeroproof · cited by 1
- ENNReal.HolderTriple.inv_sub_inv_eq_inv'proof · cited by 0