Nuprl Lemma : rn-metric_wf
∀[n:ℕ]. (rn-metric(n) ∈ metric(ℝ^n))
Proof
Definitions occuring in Statement : 
rn-metric: rn-metric(n)
, 
real-vec: ℝ^n
, 
metric: metric(X)
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
rn-metric: rn-metric(n)
, 
subtype_rel: A ⊆r B
, 
metric: metric(X)
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
all: ∀x:A. B[x]
, 
prop: ℙ
, 
uimplies: b supposing a
, 
uiff: uiff(P;Q)
, 
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced : 
real-vec-dist_wf, 
real-vec_wf, 
real-vec-dist-nonneg, 
real-vec-dist-same-zero, 
rleq_wf, 
int-to-real_wf, 
radd_wf, 
req_wf, 
istype-nat, 
real-vec-dist-symmetry, 
real-vec-triangle-inequality, 
rleq_functionality, 
req_weakening, 
radd_functionality
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
cut, 
sqequalRule, 
lambdaEquality_alt, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
applyEquality, 
setElimination, 
rename, 
inhabitedIsType, 
equalityTransitivity, 
equalitySymmetry, 
universeIsType, 
dependent_set_memberEquality_alt, 
lambdaFormation_alt, 
independent_pairFormation, 
because_Cache, 
productIsType, 
functionIsType, 
natural_numberEquality, 
axiomEquality, 
independent_isectElimination, 
productElimination
Latex:
\mforall{}[n:\mBbbN{}].  (rn-metric(n)  \mmember{}  metric(\mBbbR{}\^{}n))
Date html generated:
2019_10_30-AM-08_31_49
Last ObjectModification:
2019_10_02-AM-09_44_53
Theory : reals
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