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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