Nuprl Lemma : poly-int-val_wf2
∀[n:ℕ]. ∀[l:{l:ℤ List| ||l|| = n ∈ ℤ} ]. ∀[p:polynom(n)]. (p@l ∈ ℤ)
Proof
Definitions occuring in Statement :
poly-int-val: p@l,
polynom: polynom(n),
length: ||as||,
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
nat: ℕ,
so_lambda: λ2x.t[x],
prop: ℙ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
nat_wf,
list_wf,
set_wf,
polynom_wf,
polynom_subtype_polyform,
int_subtype_base,
list_subtype_base,
equal-wf-base-T,
poly-int-val_wf
Rules used in proof :
lambdaEquality,
because_Cache,
isect_memberEquality,
axiomEquality,
equalitySymmetry,
equalityTransitivity,
independent_isectElimination,
applyEquality,
baseClosed,
closedConclusion,
baseApply,
sqequalRule,
intEquality,
hypothesis,
dependent_set_memberEquality,
rename,
setElimination,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[l:\{l:\mBbbZ{} List| ||l|| = n\} ]. \mforall{}[p:polynom(n)]. (p@l \mmember{} \mBbbZ{})
Date html generated:
2017_04_17-AM-09_04_51
Last ObjectModification:
2017_04_13-PM-01_21_36
Theory : list_1
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