### Nuprl Lemma : diverges_wf

`∀[x:ℕ ⟶ ℝ]. (n.x[n]↑ ∈ ℙ)`

Proof

Definitions occuring in Statement :  diverges: `n.x[n]↑` real: `ℝ` nat: `ℕ` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s]` member: `t ∈ T` function: `x:A ⟶ B[x]`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` diverges: `n.x[n]↑` so_lambda: `λ2x.t[x]` prop: `ℙ` and: `P ∧ Q` nat: `ℕ` so_apply: `x[s]` exists: `∃x:A. B[x]` all: `∀x:A. B[x]`
Lemmas referenced :  exists_wf real_wf rless_wf int-to-real_wf all_wf nat_wf le_wf rleq_wf rabs_wf rsub_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesis lambdaEquality productEquality natural_numberEquality hypothesisEquality because_Cache setElimination rename applyEquality axiomEquality equalityTransitivity equalitySymmetry functionEquality

Latex:
\mforall{}[x:\mBbbN{}  {}\mrightarrow{}  \mBbbR{}].  (n.x[n]\muparrow{}  \mmember{}  \mBbbP{})

Date html generated: 2016_05_18-AM-07_36_12
Last ObjectModification: 2015_12_28-AM-00_57_04

Theory : reals

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