Nuprl Lemma : polyvar_wf2
∀[n:ℕ]. ∀[v:ℤ]. polyvar(n;v) ∈ polynom(n) supposing 0 < n
Proof
Definitions occuring in Statement :
polyvar: polyvar(n;v),
polynom: polynom(n),
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n,
int: ℤ
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,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
polynom: polynom(n),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
subtype_rel: A ⊆r B,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
polyform-lead-nonzero: polyform-lead-nonzero(n;p),
polyform: polyform(n),
polyvar: polyvar(n;v),
true: True,
has-value: (a)↓,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
poly-zero: poly-zero(n;p)
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,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
polyvar_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
nil_wf,
polynom_wf,
le_wf,
length_of_nil_lemma,
polyform-lead-nonzero_wf,
subtype_rel_list,
polyform_wf,
polynom_subtype_polyform,
decidable__lt,
top_wf,
value-type-has-value,
int-value-type,
decidable__equal_int,
polyform-value-type,
polyconst_wf,
cons_wf,
polyconst_wf2,
length_of_cons_lemma,
reduce_hd_cons_lemma,
assert_wf,
poly-zero_wf,
nat_wf,
length_upto,
upto_wf,
int_seg_wf,
equal-wf-base,
all_wf,
list_wf,
assert-poly-zero,
not_wf,
polyconst-val,
list_subtype_base,
int_subtype_base,
false_wf,
null_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
imageElimination,
productElimination,
because_Cache,
unionElimination,
equalityElimination,
applyEquality,
promote_hyp,
instantiate,
cumulativity,
dependent_set_memberEquality,
lessCases,
sqequalAxiom,
imageMemberEquality,
baseClosed,
callbyvalueReduce,
int_eqReduceTrueSq,
int_eqReduceFalseSq,
baseApply,
closedConclusion,
setEquality,
addLevel,
impliesFunctionality,
levelHypothesis
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[v:\mBbbZ{}]. polyvar(n;v) \mmember{} polynom(n) supposing 0 < n
Date html generated:
2017_09_29-PM-06_03_53
Last ObjectModification:
2017_04_26-PM-02_05_19
Theory : integer!polynomials
Home
Index