Nuprl Lemma : HofstadterF_wf
∀n:ℤ. (HofstadterF(n) ∈ if 0 <z n then ℕn + 1 else ℕ+2 fi )
Proof
Definitions occuring in Statement :
HofstadterF: HofstadterF(n),
int_seg: {i..j-},
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
all: ∀x:A. B[x],
member: t ∈ T,
add: n + m,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
and: P ∧ Q
Lemmas referenced :
Hofstadter_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
equalityTransitivity,
equalitySymmetry,
intEquality
Latex:
\mforall{}n:\mBbbZ{}. (HofstadterF(n) \mmember{} if 0 <z n then \mBbbN{}n + 1 else \mBbbN{}\msupplus{}2 fi )
Date html generated:
2018_05_21-PM-09_08_10
Last ObjectModification:
2018_05_19-PM-05_09_40
Theory : general
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