Nuprl Lemma : next-unfold
∀[k,p:Top]. ((next i > k s.t. ↑p[i]) ~ eval j = k + 1 in if p[j] then j else (next i > j s.t. ↑p[i]) fi )
Proof
Definitions occuring in Statement :
next: (next i > k s.t. ↑p[i]),
callbyvalue: callbyvalue,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
next: (next i > k s.t. ↑p[i])
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesis,
sqequalAxiom,
lemma_by_obid,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[k,p:Top].
((next i > k s.t. \muparrow{}p[i]) \msim{} eval j = k + 1 in
if p[j] then j else (next i > j s.t. \muparrow{}p[i]) fi )
Date html generated:
2016_05_15-PM-03_59_50
Last ObjectModification:
2015_12_27-PM-03_05_34
Theory : general
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