Nuprl Lemma : Moessner-aux_wf
∀[r:CRng]. ∀[x,y:Atom]. ∀[h:PowerSeries(r)]. ∀[d:ℕ ⟶ ℕ]. ∀[k:ℕ]. (Moessner-aux(r;x;y;h;d;k) ∈ PowerSeries(r))
Proof
Definitions occuring in Statement :
Moessner-aux: Moessner-aux(r;x;y;h;d;k),
power-series: PowerSeries(X;r),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
atom: Atom,
crng: CRng
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,
Moessner-aux: Moessner-aux(r;x;y;h;d;k),
eq_int: (i =z j),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
subtract: n - m,
sum: Σ(f[x] | x < k),
sum_aux: sum_aux(k;v;i;x.f[x]),
nequal: a ≠ b ∈ T ,
decidable: Dec(P),
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
int_seg: {i..j-},
lelt: i ≤ j < k
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,
btrue_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
eq_int_wf,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
fps-mul_wf,
intformnot_wf,
intformeq_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
atom-deq_wf,
fps-set-to-one_wf,
fps-pascal_wf,
decidable__le,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
sum_wf,
le_wf,
non_neg_sum,
nat_wf,
int_seg_subtype_nat,
false_wf,
int_seg_wf,
int_seg_properties,
power-series_wf,
crng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
unionElimination,
equalityElimination,
productElimination,
because_Cache,
promote_hyp,
instantiate,
cumulativity,
atomEquality,
dependent_set_memberEquality,
applyEquality,
functionExtensionality,
applyLambdaEquality,
functionEquality
Latex:
\mforall{}[r:CRng]. \mforall{}[x,y:Atom]. \mforall{}[h:PowerSeries(r)]. \mforall{}[d:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. \mforall{}[k:\mBbbN{}].
(Moessner-aux(r;x;y;h;d;k) \mmember{} PowerSeries(r))
Date html generated:
2018_05_21-PM-10_13_44
Last ObjectModification:
2017_07_26-PM-06_35_27
Theory : power!series
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