Theorems · Theorem · information theory
Real.deriv_qaryEntropy
∀ {q : ℕ} {p : ℝ}, p ≠ 0 → p ≠ 1 → deriv (Real.qaryEntropy q) p = Real.log (↑q - 1) + Real.log (1 - p) - Real.log p- Cited by
- 6 results in Mathlib
- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Realstatement and proof · cited by 25,697
- one_mulproof · cited by 2,841
- Real.logstatement and proof · cited by 939
- derivstatement and proof · cited by 676
- Int.cast_natCastproof · cited by 393
- Int.cast_oneproof · cited by 371
- Int.cast_subproof · cited by 78
- add_sub_assocproof · cited by 72
- differentiableAt_idproof · cited by 63
- deriv_id''proof · cited by 22
- Real.qaryEntropystatement · cited by 18
- deriv_fun_addproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- Real.deriv2_qaryEntropyproof · cited by 2
- Real.qaryEntropy_strictAntiOnproof · cited by 1
- Real.qaryEntropy_strictMonoOnproof · cited by 1
- Real.not_continuousAt_deriv_qaryEntropy_oneproof · cited by 0
- Real.not_continuousAt_deriv_qaryEntropy_zeroproof · cited by 0
- Real.hasDerivAt_qaryEntropyproof · cited by 0