Nuprl Lemma : decide-ifthenelse
∀[b,f1,f2,x,y:Top].
(case if b then x else y fi of inl(z) => f1[z] | inr(z) => f2[z] ~ if b
then case x of inl(z) => f1[z] | inr(z) => f2[z]
else case y of inl(z) => f1[z] | inr(z) => f2[z]
fi )
Proof
Definitions occuring in Statement :
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
sqequal: s ~ t
Definitions unfolded in proof :
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s]
Lemmas referenced :
lifting-decide-decide,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
because_Cache,
isect_memberFormation,
introduction,
sqequalAxiom
Latex:
\mforall{}[b,f1,f2,x,y:Top].
(case if b then x else y fi of inl(z) => f1[z] | inr(z) => f2[z] \msim{} if b
then case x of inl(z) => f1[z] | inr(z) => f2[z]
else case y of inl(z) => f1[z] | inr(z) => f2[z]
fi )
Date html generated:
2016_05_15-PM-02_16_02
Last ObjectModification:
2015_12_27-AM-00_31_57
Theory : untyped!computation
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