Nuprl Lemma : mdiverges_wf
∀[X:Type]. ∀[d:X ⟶ X ⟶ ℝ]. ∀[x:ℕ ⟶ X]. (n.x[n]↑ ∈ ℙ)
Proof
Definitions occuring in Statement :
mdiverges: 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],
universe: Type
Definitions unfolded in proof :
mdiverges: n.x[n]↑,
mdist: mdist(d;x;y),
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
exists: ∃x:A. B[x],
and: P ∧ Q,
all: ∀x:A. B[x],
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
real_wf,
rless_wf,
int-to-real_wf,
nat_wf,
le_wf,
rleq_wf,
istype-nat,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
productEquality,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesisEquality,
functionEquality,
setElimination,
rename,
because_Cache,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[d:X {}\mrightarrow{} X {}\mrightarrow{} \mBbbR{}]. \mforall{}[x:\mBbbN{} {}\mrightarrow{} X]. (n.x[n]\muparrow{} \mmember{} \mBbbP{})
Date html generated:
2019_10_30-AM-06_41_29
Last ObjectModification:
2019_10_02-AM-10_54_09
Theory : reals
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