Nuprl Lemma : poly-int-value
∀[p:tree(ℤ)]. ∀[l:Top List]. (p@l = p@[] ∈ ℤ) supposing ↑poly-int(p)
Proof
Definitions occuring in Statement :
poly-int-val: p@l,
poly-int: poly-int(p),
tree: tree(E),
nil: [],
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
int: ℤ,
equal: s = t ∈ T
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,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
ext-eq: A ≡ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
tree_leaf: tree_leaf(value),
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
tree_node: tree_node(left;right),
poly-int-val: p@l,
poly-val-fun: poly-val-fun(p),
tree_ind: tree_ind,
poly-int: poly-int(p),
nil: [],
tree_size: tree_size(p),
has-value: (a)↓
Lemmas referenced :
nat_properties,
full-omega-unsat,
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,
list_wf,
top_wf,
assert_wf,
poly-int_wf,
le_wf,
tree_size_wf,
tree_wf,
int_seg_wf,
int_seg_properties,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
decidable__equal_int,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
intformeq_wf,
int_formula_prop_eq_lemma,
decidable__lt,
lelt_wf,
subtype_rel_self,
itermAdd_wf,
int_term_value_add_lemma,
nat_wf,
tree-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
atom_subtype_base,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
reduce_tl_nil_lemma,
assert_of_band,
poly-zero_wf,
poly-zero-val,
tl_wf,
value-type-has-value,
list-value-type,
int-value-type
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
because_Cache,
productElimination,
unionElimination,
instantiate,
applyLambdaEquality,
dependent_set_memberEquality,
hypothesis_subsumption,
isect_memberFormation,
addEquality,
promote_hyp,
tokenEquality,
equalityElimination,
cumulativity,
atomEquality,
callbyvalueReduce,
sqleReflexivity
Latex:
\mforall{}[p:tree(\mBbbZ{})]. \mforall{}[l:Top List]. (p@l = p@[]) supposing \muparrow{}poly-int(p)
Date html generated:
2018_05_21-PM-06_18_52
Last ObjectModification:
2018_05_19-PM-05_34_59
Theory : integer!polynomial!trees
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