Nuprl Lemma : mcomplete_wf
∀[M:MetricSpace]. (mcomplete(M) ∈ ℙ)
Proof
Definitions occuring in Statement :
mcomplete: mcomplete(M),
metric-space: MetricSpace,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mcomplete: mcomplete(M),
metric-space: MetricSpace,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
metric_wf,
nat_wf,
mcauchy_wf,
istype-nat,
mconverges_wf,
metric-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
spreadEquality,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairEquality_alt,
hypothesisEquality,
universeIsType,
extract_by_obid,
isectElimination,
hypothesis,
functionEquality,
lambdaEquality_alt,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[M:MetricSpace]. (mcomplete(M) \mmember{} \mBbbP{})
Date html generated:
2019_10_30-AM-06_42_10
Last ObjectModification:
2019_10_02-AM-10_54_44
Theory : reals
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