Nuprl Lemma : mcomplete-rn-prod-metric
∀n:ℕ. mcomplete(ℝ^n with rn-prod-metric(n))
Proof
Definitions occuring in Statement :
rn-prod-metric: rn-prod-metric(n),
real-vec: ℝ^n,
mcomplete: mcomplete(M),
mk-metric-space: X with d,
nat: ℕ,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
implies: P ⇒ Q,
mcomplete: mcomplete(M),
mk-metric-space: X with d,
prod-metric-space: prod-metric-space(k;X),
pi1: fst(t),
pi2: snd(t),
rn-prod-metric: rn-prod-metric(n),
real-vec: ℝ^n
Lemmas referenced :
prod-metric-space-complete,
mk-metric-space_wf,
real_wf,
rmetric_wf,
int_seg_wf,
reals-complete,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
lambdaEquality_alt,
isectElimination,
hypothesis,
universeIsType,
natural_numberEquality,
setElimination,
rename,
independent_functionElimination,
sqequalRule
Latex:
\mforall{}n:\mBbbN{}. mcomplete(\mBbbR{}\^{}n with rn-prod-metric(n))
Date html generated:
2019_10_30-AM-08_33_37
Last ObjectModification:
2019_10_02-AM-11_01_06
Theory : reals
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