Nuprl Lemma : mconverges_wf
∀[X:Type]. ∀[d:X ⟶ X ⟶ ℝ]. ∀[x:ℕ ⟶ X]. (x[n]↓ as n→∞ ∈ ℙ)
Proof
Definitions occuring in Statement :
mconverges: x[n]↓ as 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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mconverges: x[n]↓ as n→∞,
prop: ℙ,
exists: ∃x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
mconverges-to_wf,
istype-nat,
real_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality_alt,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
because_Cache,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[d:X {}\mrightarrow{} X {}\mrightarrow{} \mBbbR{}]. \mforall{}[x:\mBbbN{} {}\mrightarrow{} X]. (x[n]\mdownarrow{} as n\mrightarrow{}\minfty{} \mmember{} \mBbbP{})
Date html generated:
2019_10_30-AM-06_40_09
Last ObjectModification:
2019_10_02-AM-10_52_55
Theory : reals
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