### Nuprl Lemma : infinite-deriv-seq_wf

`∀[I:Interval]. ∀[F:ℕ ⟶ I ⟶ℝ].  (infinite-deriv-seq(I;i,x.F[i;x]) ∈ ℙ)`

Proof

Definitions occuring in Statement :  infinite-deriv-seq: `infinite-deriv-seq(I;i,x.F[i; x])` rfun: `I ⟶ℝ` interval: `Interval` nat: `ℕ` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s1;s2]` member: `t ∈ T` function: `x:A ⟶ B[x]`
Definitions unfolded in proof :  and: `P ∧ Q` top: `Top` not: `¬A` implies: `P `` Q` false: `False` exists: `∃x:A. B[x]` satisfiable_int_formula: `satisfiable_int_formula(fmla)` uimplies: `b supposing a` or: `P ∨ Q` decidable: `Dec(P)` all: `∀x:A. B[x]` ge: `i ≥ j ` nat: `ℕ` so_apply: `x[s]` prop: `ℙ` subtype_rel: `A ⊆r B` so_apply: `x[s1;s2]` rfun: `I ⟶ℝ` label: `...\$L... t` so_lambda: `λ2x.t[x]` infinite-deriv-seq: `infinite-deriv-seq(I;i,x.F[i; x])` member: `t ∈ T` uall: `∀[x:A]. B[x]`
Lemmas referenced :  all_wf nat_wf derivative_wf rfun_wf real_wf i-member_wf nat_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermAdd_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_add_lemma int_term_value_var_lemma int_formula_prop_wf le_wf interval_wf
Rules used in proof :  functionEquality equalitySymmetry equalityTransitivity axiomEquality because_Cache computeAll independent_pairFormation voidEquality voidElimination isect_memberEquality intEquality int_eqEquality dependent_pairFormation independent_isectElimination unionElimination dependent_functionElimination natural_numberEquality rename setElimination addEquality dependent_set_memberEquality setEquality applyEquality hypothesisEquality lambdaEquality hypothesis thin isectElimination sqequalHypSubstitution lemma_by_obid sqequalRule cut introduction isect_memberFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution

Latex:
\mforall{}[I:Interval].  \mforall{}[F:\mBbbN{}  {}\mrightarrow{}  I  {}\mrightarrow{}\mBbbR{}].    (infinite-deriv-seq(I;i,x.F[i;x])  \mmember{}  \mBbbP{})

Date html generated: 2016_05_18-AM-10_28_13
Last ObjectModification: 2016_01_17-AM-00_25_56

Theory : reals

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