Nuprl Lemma : sq_stable__polyform-lead-nonzero
∀n:ℕ. ∀p:polyform(n). SqStable(polyform-lead-nonzero(n;p))
Proof
Definitions occuring in Statement :
polyform-lead-nonzero: polyform-lead-nonzero(n;p),
polyform: polyform(n),
nat: ℕ,
sq_stable: SqStable(P),
all: ∀x:A. B[x]
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),
so_apply: x[s],
and: P ∧ Q,
top: Top,
not: ¬A,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
ge: i ≥ j ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
prop: ℙ,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
polyform-lead-nonzero: polyform-lead-nonzero(n;p),
polyform: polyform(n),
all: ∀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,
sq_stable__not,
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,
sq_stable__all,
eq_int_wf,
nat_wf,
polyform_wf
Rules used in proof :
impliesFunctionality,
cumulativity,
instantiate,
productElimination,
imageElimination,
unionElimination,
dependent_set_memberEquality,
baseClosed,
independent_functionElimination,
computeAll,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
dependent_functionElimination,
intEquality,
int_eqEquality,
dependent_pairFormation,
independent_isectElimination,
functionEquality,
lambdaEquality,
equalitySymmetry,
equalityTransitivity,
because_Cache,
natural_numberEquality,
rename,
setElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
extract_by_obid,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}n:\mBbbN{}. \mforall{}p:polyform(n). SqStable(polyform-lead-nonzero(n;p))
Date html generated:
2017_04_17-AM-09_02_48
Last ObjectModification:
2017_04_13-PM-00_40_29
Theory : list_1
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