Nuprl Lemma : Moessner_wf
∀[r:CRng]. ∀[x,y:Atom]. ∀[h:PowerSeries(r)]. ∀[d:ℕ ⟶ ℕ]. ∀[k:ℕ]. (Moessner(r;x;y;h;d;k) ∈ PowerSeries(r))
Proof
Definitions occuring in Statement :
Moessner: Moessner(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,
Moessner: Moessner(r;x;y;h;d;k),
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
so_apply: x[s]
Lemmas referenced :
crng_wf,
power-series_wf,
Moessner-aux_wf,
int_seg_wf,
nat_wf,
false_wf,
int_seg_subtype_nat,
le_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
sum_wf,
fps-slice_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
atomEquality,
hypothesisEquality,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
natural_numberEquality,
hypothesis,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
applyEquality,
lambdaFormation,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality
Latex:
\mforall{}[r:CRng]. \mforall{}[x,y:Atom]. \mforall{}[h:PowerSeries(r)]. \mforall{}[d:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. \mforall{}[k:\mBbbN{}].
(Moessner(r;x;y;h;d;k) \mmember{} PowerSeries(r))
Date html generated:
2016_05_15-PM-10_01_04
Last ObjectModification:
2016_01_16-PM-03_06_51
Theory : power!series
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