Nuprl Lemma : poly-zero_wf
∀[n:ℕ]. ∀[p:polyform(n)]. (poly-zero(n;p) ∈ 𝔹)
Proof
Definitions occuring in Statement :
poly-zero: poly-zero(n;p),
polyform: polyform(n),
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
guard: {T},
sq_type: SQType(T),
top: Top,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
false: False,
rev_implies: P ⇐ Q,
prop: ℙ,
not: ¬A,
iff: P ⇐⇒ Q,
bfalse: ff,
polyform: polyform(n),
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
implies: P ⇒ Q,
all: ∀x:A. B[x],
nat: ℕ,
poly-zero: poly-zero(n;p),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
bool_subtype_base,
subtype_base_sq,
bool_cases,
le_wf,
int_formula_prop_wf,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformeq_wf,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
subtract_wf,
null_wf,
nat_wf,
polyform_wf,
equal_wf,
assert_of_bnot,
eqff_to_assert,
iff_weakening_uiff,
not_wf,
bnot_wf,
iff_transitivity,
assert_of_eq_int,
eqtt_to_assert,
assert_wf,
equal-wf-T-base,
uiff_transitivity,
bool_wf,
eq_int_wf
Rules used in proof :
cumulativity,
instantiate,
computeAll,
voidEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
dependent_set_memberEquality,
voidElimination,
isect_memberEquality,
axiomEquality,
dependent_functionElimination,
impliesFunctionality,
independent_pairFormation,
independent_isectElimination,
productElimination,
independent_functionElimination,
intEquality,
because_Cache,
baseClosed,
equalitySymmetry,
equalityTransitivity,
equalityElimination,
unionElimination,
lambdaFormation,
natural_numberEquality,
hypothesis,
hypothesisEquality,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[p:polyform(n)]. (poly-zero(n;p) \mmember{} \mBbbB{})
Date html generated:
2017_04_17-AM-09_02_02
Last ObjectModification:
2017_04_13-AM-11_53_40
Theory : list_1
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