Nuprl Lemma : polyform-lead-nonzero_wf
∀[n:ℕ]. ∀[p:polyform(n)]. (polyform-lead-nonzero(n;p) ∈ ℙ)
Proof
Definitions occuring in Statement :
polyform-lead-nonzero: polyform-lead-nonzero(n;p),
polyform: polyform(n),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
bfalse: ff,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
guard: {T},
sq_type: SQType(T),
squash: ↓T,
less_than: a < b,
or: P ∨ Q,
decidable: Dec(P),
and: P ∧ Q,
top: Top,
all: ∀x:A. B[x],
not: ¬A,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
ge: i ≥ j ,
prop: ℙ,
implies: P ⇒ Q,
nat: ℕ,
polyform-lead-nonzero: polyform-lead-nonzero(n;p),
polyform: polyform(n),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
assert_of_bnot,
iff_weakening_uiff,
iff_transitivity,
eqff_to_assert,
assert_of_eq_int,
eqtt_to_assert,
bool_subtype_base,
bool_wf,
subtype_base_sq,
bool_cases,
le_wf,
int_term_value_subtract_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformle_wf,
intformnot_wf,
decidable__le,
subtract_wf,
length_wf,
equal-wf-T-base,
bnot_wf,
hd_wf,
poly-zero_wf,
assert_wf,
not_wf,
int_formula_prop_wf,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_and_lemma,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformless_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties,
less_than_wf,
eq_int_wf,
nat_wf,
polyform_wf
Rules used in proof :
impliesFunctionality,
lambdaFormation,
independent_functionElimination,
cumulativity,
instantiate,
productElimination,
imageElimination,
unionElimination,
dependent_set_memberEquality,
baseClosed,
computeAll,
independent_pairFormation,
voidEquality,
voidElimination,
dependent_functionElimination,
intEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
independent_isectElimination,
functionEquality,
natural_numberEquality,
rename,
setElimination,
because_Cache,
isect_memberEquality,
hypothesisEquality,
thin,
isectElimination,
extract_by_obid,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
sqequalRule,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[p:polyform(n)]. (polyform-lead-nonzero(n;p) \mmember{} \mBbbP{})
Date html generated:
2017_04_17-AM-09_02_33
Last ObjectModification:
2017_04_13-PM-00_36_05
Theory : list_1
Home
Index