Nuprl Lemma : rn-prod-metric_wf
∀[n:ℕ]. (rn-prod-metric(n) ∈ metric(ℝ^n))
Proof
Definitions occuring in Statement :
rn-prod-metric: rn-prod-metric(n),
real-vec: ℝ^n,
metric: metric(X),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
real-vec: ℝ^n,
uall: ∀[x:A]. B[x],
member: t ∈ T,
rn-prod-metric: rn-prod-metric(n),
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
prod-metric_wf,
real_wf,
int_seg_wf,
rmetric_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality_alt,
hypothesis,
universeIsType,
natural_numberEquality,
setElimination,
rename,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[n:\mBbbN{}]. (rn-prod-metric(n) \mmember{} metric(\mBbbR{}\^{}n))
Date html generated:
2019_10_30-AM-08_33_10
Last ObjectModification:
2019_10_02-AM-11_00_47
Theory : reals
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