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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