### Nuprl Lemma : derived-seq_wf

`∀[T:Type]. ∀[f:ℕ ⟶ T]. ∀[s:k:ℕ × (ℕk ⟶ ℕ)].  (derived-seq(f;s) ∈ ℕ ⟶ (k:ℕ × (ℕk ⟶ T)))`

Proof

Definitions occuring in Statement :  derived-seq: `derived-seq(f;s)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` product: `x:A × B[x]` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  derived-seq: `derived-seq(f;s)` uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` subtype_rel: `A ⊆r B` all: `∀x:A. B[x]` implies: `P `` Q` guard: `{T}` int_seg: `{i..j-}` ge: `i ≥ j ` lelt: `i ≤ j < k` and: `P ∧ Q` decidable: `Dec(P)` or: `P ∨ Q` false: `False` uiff: `uiff(P;Q)` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` top: `Top` prop: `ℙ`
Lemmas referenced :  nat_wf int_seg_wf add_nat_wf nat_properties int_seg_properties decidable__le add-is-int-iff satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf itermAdd_wf intformeq_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_term_value_add_lemma int_formula_prop_eq_lemma int_formula_prop_wf false_wf equal_wf le_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut productElimination thin lambdaEquality dependent_pairEquality hypothesisEquality applyEquality functionExtensionality extract_by_obid hypothesis dependent_set_memberEquality addEquality sqequalHypSubstitution setElimination rename isectElimination natural_numberEquality because_Cache lambdaFormation equalityTransitivity equalitySymmetry applyLambdaEquality dependent_functionElimination unionElimination pointwiseFunctionality promote_hyp baseApply closedConclusion baseClosed independent_isectElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination functionEquality cumulativity axiomEquality productEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[f:\mBbbN{}  {}\mrightarrow{}  T].  \mforall{}[s:k:\mBbbN{}  \mtimes{}  (\mBbbN{}k  {}\mrightarrow{}  \mBbbN{})].    (derived-seq(f;s)  \mmember{}  \mBbbN{}  {}\mrightarrow{}  (k:\mBbbN{}  \mtimes{}  (\mBbbN{}k  {}\mrightarrow{}  T)))

Date html generated: 2018_05_21-PM-07_41_51
Last ObjectModification: 2017_07_26-PM-05_15_43

Theory : general

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