Nuprl Lemma : poly-val-fun_wf
∀[n:ℕ]. ∀[p:polyform(n)]. (poly-val-fun(p) ∈ {l:ℤ List| n ≤ ||l||} ⟶ ℤ)
Proof
Definitions occuring in Statement :
poly-val-fun: poly-val-fun(p),
polyform: polyform(n),
length: ||as||,
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
le: A ≤ B,
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
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,
top: Top,
and: P ∧ Q,
prop: ℙ,
polyform: polyform(n),
subtype_rel: A ⊆r B,
ext-eq: A ≡ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
sq_type: SQType(T),
guard: {T},
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
tree_leaf: tree_leaf(value),
tree_size: tree_size(p),
poly-val-fun: poly-val-fun(p),
tree_ind: tree_ind,
bfalse: ff,
or: P ∨ Q,
bnot: ¬bb,
assert: ↑b,
tree_node: tree_node(left;right),
cand: A c∧ B,
decidable: Dec(P),
le: A ≤ B,
cons: [a / b],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
has-value: (a)↓
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,
le_wf,
tree_size_wf,
nat_wf,
polyform_wf,
tree-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
list_wf,
length_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
le_weakening2,
decidable__lt,
itermAdd_wf,
int_term_value_add_lemma,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
ispolyform_node_lemma,
assert_wf,
band_wf,
ispolyform_wf,
lt_int_wf,
list-cases,
length_of_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
reduce_tl_cons_lemma,
reduce_hd_cons_lemma,
iff_transitivity,
iff_weakening_uiff,
assert_of_band,
assert_of_lt_int,
value-type-has-value,
list-value-type,
int-value-type,
add-is-int-iff,
false_wf,
cons_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
isect_memberFormation,
promote_hyp,
productElimination,
hypothesis_subsumption,
tokenEquality,
unionElimination,
equalityElimination,
instantiate,
cumulativity,
atomEquality,
because_Cache,
setEquality,
applyLambdaEquality,
productEquality,
dependent_set_memberEquality,
callbyvalueReduce,
functionExtensionality,
pointwiseFunctionality,
baseApply,
closedConclusion,
baseClosed,
addEquality,
multiplyEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[p:polyform(n)]. (poly-val-fun(p) \mmember{} \{l:\mBbbZ{} List| n \mleq{} ||l||\} {}\mrightarrow{} \mBbbZ{})
Date html generated:
2017_10_01-AM-08_32_28
Last ObjectModification:
2017_05_02-PM-04_24_40
Theory : integer!polynomial!trees
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