Nuprl Lemma : insert-combine-cons
∀cmp,f,x,a,as:Top.
(insert-combine(cmp;f;x;[a / as]) ~ eval tst = cmp x a in
if (tst =z 0) then [f x a / as]
if 0 <z tst then [x; [a / as]]
else [a / insert-combine(cmp;f;x;as)]
fi )
Proof
Definitions occuring in Statement :
insert-combine: insert-combine(cmp;f;x;l),
cons: [a / b],
callbyvalue: callbyvalue,
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
eq_int: (i =z j),
top: Top,
all: ∀x:A. B[x],
apply: f a,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
insert-combine: insert-combine(cmp;f;x;l),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
member: t ∈ T,
top: Top,
so_apply: x[s1;s2;s3]
Lemmas referenced :
list_ind_cons_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis
Latex:
\mforall{}cmp,f,x,a,as:Top.
(insert-combine(cmp;f;x;[a / as]) \msim{} eval tst = cmp x a in
if (tst =\msubz{} 0) then [f x a / as]
if 0 <z tst then [x; [a / as]]
else [a / insert-combine(cmp;f;x;as)]
fi )
Date html generated:
2016_05_14-PM-02_40_52
Last ObjectModification:
2015_12_26-PM-02_44_15
Theory : list_1
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