### Nuprl Lemma : regular-int-seq_wf

`∀[k:ℤ]. ∀[f:ℕ+ ⟶ ℤ].  (k-regular-seq(f) ∈ ℙ)`

Proof

Definitions occuring in Statement :  regular-int-seq: `k-regular-seq(f)` nat_plus: `ℕ+` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` regular-int-seq: `k-regular-seq(f)` so_lambda: `λ2x.t[x]` nat_plus: `ℕ+` subtype_rel: `A ⊆r B` nat: `ℕ` so_apply: `x[s]`
Lemmas referenced :  all_wf nat_plus_wf le_wf absval_wf subtract_wf nat_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesis lambdaEquality multiplyEquality setElimination rename hypothesisEquality applyEquality natural_numberEquality addEquality axiomEquality equalityTransitivity equalitySymmetry functionEquality intEquality isect_memberEquality because_Cache

Latex:
\mforall{}[k:\mBbbZ{}].  \mforall{}[f:\mBbbN{}\msupplus{}  {}\mrightarrow{}  \mBbbZ{}].    (k-regular-seq(f)  \mmember{}  \mBbbP{})

Date html generated: 2016_05_18-AM-06_46_14
Last ObjectModification: 2015_12_28-AM-00_24_44

Theory : reals

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