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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