Nuprl Lemma : mFOL-hyps-meaning-cons
∀[hyps,Dom,S,a,x:Top].
(tuple-type(mFOL-hyps-meaning(Dom;S;a;[x / hyps])) ~ if null(hyps)
then Dom,S,a |= mFOL-abstract(x)
else Dom,S,a |= mFOL-abstract(x) × tuple-type(mFOL-hyps-meaning(Dom;S;a;hyps))
fi )
Proof
Definitions occuring in Statement :
mFOL-hyps-meaning: mFOL-hyps-meaning(Dom;S;a;hyps),
mFOL-abstract: mFOL-abstract(fmla),
FOSatWith: Dom,S,a |= fmla,
tuple-type: tuple-type(L),
null: null(as),
cons: [a / b],
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
product: x:A × B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mFOL-hyps-meaning: mFOL-hyps-meaning(Dom;S;a;hyps),
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
map_cons_lemma,
tupletype_cons_lemma,
null-map,
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,
isectElimination,
hypothesisEquality,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[hyps,Dom,S,a,x:Top].
(tuple-type(mFOL-hyps-meaning(Dom;S;a;[x / hyps])) \msim{} if null(hyps)
then Dom,S,a |= mFOL-abstract(x)
else Dom,S,a |= mFOL-abstract(x) \mtimes{} tuple-type(mFOL-hyps-meaning(Dom;S;a;hyps))
fi )
Date html generated:
2016_05_15-PM-10_26_41
Last ObjectModification:
2015_12_27-PM-06_26_38
Theory : minimal-first-order-logic
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