Nuprl Lemma : poly_int_val_cons
∀p,l,a:Top. (p@[a / l] ~ Σ(p[i]@l * a^||p|| - 1 - i | i < ||p||))
Proof
Definitions occuring in Statement :
poly-int-val: p@l,
exp: i^n,
sum: Σ(f[x] | x < k),
select: L[n],
length: ||as||,
cons: [a / b],
top: Top,
all: ∀x:A. B[x],
multiply: n * m,
subtract: n - m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
bfalse: ff,
ifthenelse: if b then t else f fi ,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
top: Top,
poly-int-val: p@l,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
spread_cons_lemma,
null_cons_lemma,
top_wf
Rules used in proof :
voidEquality,
voidElimination,
isect_memberEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
sqequalRule,
extract_by_obid,
introduction,
hypothesis,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}p,l,a:Top. (p@[a / l] \msim{} \mSigma{}(p[i]@l * a\^{}||p|| - 1 - i | i < ||p||))
Date html generated:
2017_04_20-AM-07_08_30
Last ObjectModification:
2017_04_17-AM-11_46_20
Theory : list_1
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