### 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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