Nuprl Lemma : howard-bar-rec-equal-decidable
∀[M,mon,base,ind:Top]. ∀[n:ℕ]. ∀[s:Top].
(howard-bar-rec(M;mon;base;ind;n;s) ~ decidable-bar-rec(M;λn,s,r. let k,p = r in base n s (mon n k s p);ind;n;s))
Proof
Definitions occuring in Statement :
howard-bar-rec: howard-bar-rec(M;mon;base;ind;n;s),
decidable-bar-rec: decidable-bar-rec(dec;base;ind;n;s),
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
lambda: λx.A[x],
spread: spread def,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
howard-bar-rec: howard-bar-rec(M;mon;base;ind;n;s),
decidable-bar-rec: decidable-bar-rec(dec;base;ind;n;s)
Lemmas referenced :
top_wf,
nat_wf
Rules used in proof :
hypothesisEquality,
thin,
isectElimination,
isect_memberEquality,
sqequalHypSubstitution,
sqequalAxiom,
introduction,
isect_memberFormation,
because_Cache,
hypothesis,
lemma_by_obid,
cut,
sqequalRule,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[M,mon,base,ind:Top]. \mforall{}[n:\mBbbN{}]. \mforall{}[s:Top].
(howard-bar-rec(M;mon;base;ind;n;s) \msim{} decidable-bar-rec(M;\mlambda{}n,s,r. let k,p = r
in base n s (mon n k s p);ind;n;\000Cs))
Date html generated:
2016_05_19-PM-00_08_20
Last ObjectModification:
2016_05_18-PM-02_16_04
Theory : continuity
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