Nuprl Lemma : polyvar-val
∀[v:ℕ]. ∀[l:{l:ℤ List| v < ||l||} ]. (polyvar(v)@l = l[v] ∈ ℤ)
Proof
Definitions occuring in Statement :
poly-int-val: p@l,
polyvar: polyvar(v),
select: L[n],
length: ||as||,
list: T List,
nat: ℕ,
less_than: a < b,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
int: ℤ,
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],
so_apply: x[s],
polyvar: polyvar(v),
decidable: Dec(P),
or: P ∨ Q,
poly-int-val: p@l,
poly-val-fun: poly-val-fun(p),
tree_node: tree_node(left;right),
tree_ind: tree_ind,
tree_leaf: tree_leaf(value),
tl: tl(l),
nil: [],
it: ⋅,
select: L[n],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
cons: [a / b],
has-value: (a)↓,
polynom: polynom(n),
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
sq_type: SQType(T),
guard: {T},
true: True,
iff: P ⇐⇒ Q,
rev_implies: 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,
length_wf,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
nat_wf,
list-cases,
length_of_nil_lemma,
stuck-spread,
base_wf,
product_subtype_list,
length_of_cons_lemma,
reduce_tl_cons_lemma,
reduce_hd_cons_lemma,
value-type-has-value,
list-value-type,
int-value-type,
decidable__equal_int,
intformeq_wf,
itermAdd_wf,
itermMultiply_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_term_value_mul_lemma,
polyvar_wf,
le_wf,
polynom_wf,
equal_wf,
polyform_wf,
value-type-polyform,
equal-wf-base,
int_subtype_base,
reduce_tl_nil_lemma,
decidable__lt,
add-is-int-iff,
false_wf,
subtype_base_sq,
squash_wf,
true_wf,
select_cons_tl,
iff_weakening_equal
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,
axiomEquality,
unionElimination,
callbyvalueReduce,
sqleReflexivity,
baseClosed,
imageElimination,
productElimination,
promote_hyp,
hypothesis_subsumption,
because_Cache,
dependent_set_memberEquality,
addEquality,
equalityTransitivity,
equalitySymmetry,
axiomSqleEquality,
applyEquality,
int_eqReduceFalseSq,
pointwiseFunctionality,
baseApply,
closedConclusion,
instantiate,
cumulativity,
universeEquality,
imageMemberEquality
Latex:
\mforall{}[v:\mBbbN{}]. \mforall{}[l:\{l:\mBbbZ{} List| v < ||l||\} ]. (polyvar(v)@l = l[v])
Date html generated:
2017_10_01-AM-08_32_33
Last ObjectModification:
2017_07_26-PM-04_25_13
Theory : integer!polynomial!trees
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