Nuprl Lemma : polyconst-val
∀[n:ℕ]. ∀[l:{l:ℤ List| ||l|| = n ∈ ℤ} ]. ∀[k:ℤ]. (polyconst(n;k)@l ~ k)
Proof
Definitions occuring in Statement :
polyconst: polyconst(n;k),
poly-int-val: p@l,
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 :
has-value: (a)↓,
uiff: uiff(P;Q),
select: L[n],
sum_aux: sum_aux(k;v;i;x.f[x]),
sum: Σ(f[x] | x < k),
subtract: n - m,
bfalse: ff,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
sq_type: SQType(T),
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
true: True,
squash: ↓T,
btrue: tt,
ifthenelse: if b then t else f fi ,
poly-int-val: p@l,
le: A ≤ B,
decidable: Dec(P),
cons: [a / b],
or: P ∨ Q,
polyconst: polyconst(n;k),
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 :
int_term_value_mul_lemma,
itermMultiply_wf,
int-value-type,
value-type-has-value,
false_wf,
add-is-int-iff,
exp0_lemma,
spread_cons_lemma,
null_cons_lemma,
poly_int_val_cons_cons,
iff_weakening_equal,
equal_wf,
poly_int_val_nil_cons,
subtype_base_sq,
decidable__equal_int,
null_nil_lemma,
nat_wf,
list_subtype_base,
equal-wf-base-T,
int_subtype_base,
length_of_nil_lemma,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
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,
list-cases,
less_than_irreflexivity,
less_than_transitivity1,
equal-wf-base,
list_wf,
set_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 :
multiplyEquality,
addEquality,
pointwiseFunctionality,
dependent_set_memberEquality,
sqleReflexivity,
callbyvalueReduce,
imageMemberEquality,
imageElimination,
cumulativity,
instantiate,
int_eqReduceFalseSq,
int_eqReduceTrueSq,
equalitySymmetry,
equalityTransitivity,
productElimination,
hypothesis_subsumption,
promote_hyp,
unionElimination,
because_Cache,
applyEquality,
baseClosed,
closedConclusion,
baseApply,
sqequalAxiom,
independent_functionElimination,
computeAll,
independent_pairFormation,
sqequalRule,
voidEquality,
voidElimination,
isect_memberEquality,
dependent_functionElimination,
intEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
independent_isectElimination,
natural_numberEquality,
lambdaFormation,
intWeakElimination,
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{}[k:\mBbbZ{}]. (polyconst(n;k)@l \msim{} k)
Date html generated:
2017_04_20-AM-07_10_34
Last ObjectModification:
2017_04_17-PM-02_10_15
Theory : list_1
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