Nuprl Lemma : find-combine-cons
∀[cmp,x,l:Top].
(find-combine(cmp;[x / l]) ~ eval tst = cmp x in
if (tst =z 0) then inl x
if 0 <z tst then inr ⋅
else find-combine(cmp;l)
fi )
Proof
Definitions occuring in Statement :
find-combine: find-combine(cmp;l),
cons: [a / b],
callbyvalue: callbyvalue,
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
eq_int: (i =z j),
it: ⋅,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
inr: inr x ,
inl: inl x,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
find-combine: find-combine(cmp;l),
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3]
Lemmas referenced :
list_ind_cons_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[cmp,x,l:Top].
(find-combine(cmp;[x / l]) \msim{} eval tst = cmp x in
if (tst =\msubz{} 0) then inl x
if 0 <z tst then inr \mcdot{}
else find-combine(cmp;l)
fi )
Date html generated:
2016_05_14-PM-02_40_28
Last ObjectModification:
2015_12_26-PM-02_44_24
Theory : list_1
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