Nuprl Lemma : poly-int-val_wf
∀[n:ℕ]. ∀[l:{l:ℤ List| ||l|| = n ∈ ℤ} ]. ∀[p:polyform(n)]. (p@l ∈ ℤ)
Proof
Definitions occuring in Statement :
poly-int-val: p@l,
polyform: polyform(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 :
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
sq_type: SQType(T),
squash: ↓T,
less_than: a < b,
uiff: uiff(P;Q),
lelt: i ≤ j < k,
int_seg: {i..j-},
bfalse: ff,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
btrue: tt,
ifthenelse: if b then t else f fi ,
poly-int-val: p@l,
less_than': less_than'(a;b),
le: A ≤ B,
decidable: Dec(P),
cons: [a / b],
polyform: polyform(n),
or: P ∨ Q,
so_apply: x[s],
guard: {T},
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
top: Top,
all: ∀x:A. B[x],
not: ¬A,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
ge: i ≥ j ,
false: False,
implies: P ⇒ Q,
nat: ℕ,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
assert_of_bnot,
iff_weakening_uiff,
iff_transitivity,
eqff_to_assert,
assert_of_eq_int,
eqtt_to_assert,
bool_subtype_base,
bool_wf,
subtype_base_sq,
bool_cases,
int_seg_wf,
exp_wf2,
select_wf,
add-is-int-iff,
decidable__equal_int,
int_seg_properties,
length_wf_nat,
sum_wf,
spread_cons_lemma,
null_cons_lemma,
le_weakening,
not_wf,
bnot_wf,
assert_wf,
null_nil_lemma,
eq_int_wf,
nat_wf,
list_subtype_base,
equal-wf-base-T,
int_subtype_base,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
le_wf,
false_wf,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
itermAdd_wf,
intformeq_wf,
decidable__lt,
non_neg_length,
length_wf,
le_weakening2,
length_of_cons_lemma,
product_subtype_list,
length_of_nil_lemma,
list-cases,
less_than_irreflexivity,
less_than_transitivity1,
equal-wf-base,
list_wf,
set_wf,
polyform_wf,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties
Rules used in proof :
impliesFunctionality,
cumulativity,
instantiate,
imageElimination,
pointwiseFunctionality,
multiplyEquality,
dependent_set_memberEquality,
productElimination,
hypothesis_subsumption,
promote_hyp,
unionElimination,
because_Cache,
applyEquality,
baseClosed,
closedConclusion,
baseApply,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
independent_functionElimination,
computeAll,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
dependent_functionElimination,
intEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
independent_isectElimination,
natural_numberEquality,
lambdaFormation,
intWeakElimination,
sqequalRule,
rename,
setElimination,
hypothesis,
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:polyform(n)]. (p@l \mmember{} \mBbbZ{})
Date html generated:
2017_04_17-AM-09_04_33
Last ObjectModification:
2017_04_13-PM-00_43_05
Theory : list_1
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