Nuprl Lemma : polyconst-val
∀[n:ℕ]. ∀[l:{l:ℤ List| ||l|| = n ∈ ℤ} ]. ∀[k:ℤ]. (l@polyconst(n;k) ~ k)
Proof
Definitions occuring in Statement :
polyconst: polyconst(n;k),
poly-int-val: l@p,
length: ||as||,
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
int: ℤ,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
guard: {T},
so_apply: x[s],
polyconst: polyconst(n;k),
or: P ∨ Q,
cons: [a / b],
decidable: Dec(P),
le: A ≤ B,
poly-int-val: l@p,
ifthenelse: if b then t else f fi ,
btrue: tt,
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
bfalse: ff,
sum: Σ(f[x] | x < k),
subtract: n - m,
sum_aux: sum_aux(k;v;i;x.f[x]),
select: L[n],
has-value: (a)↓,
uiff: uiff(P;Q)
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
set_wf,
list_wf,
equal-wf-base,
less_than_transitivity1,
less_than_irreflexivity,
list-cases,
product_subtype_list,
length_of_cons_lemma,
le_weakening2,
length_wf,
non_neg_length,
decidable__lt,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
length_of_nil_lemma,
int_subtype_base,
equal-wf-base-T,
list_subtype_base,
nat_wf,
null_nil_lemma,
decidable__equal_int,
subtype_base_sq,
poly_int_val_nil_cons,
equal_wf,
iff_weakening_equal,
poly_int_val_cons_cons,
null_cons_lemma,
spread_cons_lemma,
value-type-has-value,
int-value-type,
polyform_wf,
le_wf,
polyform-value-type,
polyconst_wf,
exp0_lemma,
add-is-int-iff,
false_wf,
itermMultiply_wf,
int_term_value_mul_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
sqequalAxiom,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
because_Cache,
unionElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
equalityTransitivity,
equalitySymmetry,
int_eqReduceTrueSq,
int_eqReduceFalseSq,
instantiate,
cumulativity,
imageElimination,
imageMemberEquality,
dependent_set_memberEquality,
callbyvalueReduce,
sqleReflexivity,
pointwiseFunctionality,
addEquality,
multiplyEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[l:\{l:\mBbbZ{} List| ||l|| = n\} ]. \mforall{}[k:\mBbbZ{}]. (l@polyconst(n;k) \msim{} k)
Date html generated:
2017_09_29-PM-06_00_25
Last ObjectModification:
2017_04_26-PM-02_04_56
Theory : integer!polynomials
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