Nuprl Lemma : rccp-compact_wf
∀[k,n:ℕ]. ∀[K:{K:n-dim-complex| 0 < ||K||} ]. (rccp-compact(k;K) ∈ mcompact(|K|;rn-prod-metric(k)))
Proof
Definitions occuring in Statement :
rccp-compact: rccp-compact(k;K),
rat-cube-complex-polyhedron: |K|,
rn-prod-metric: rn-prod-metric(n),
mcompact: mcompact(X;d),
length: ||as||,
nat: ℕ,
less_than: a < b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
natural_number: $n,
rational-cube-complex: n-dim-complex
Definitions unfolded in proof :
rat-cube-complex-polyhedron: |K|,
uimplies: b supposing a,
prop: ℙ,
rational-cube-complex: n-dim-complex,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
rccp-compact: rccp-compact(k;K),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-nat,
istype-less_than,
real-vec_wf,
metric-on-subtype,
rn-prod-metric_wf,
rat-cube-complex-polyhedron_wf,
mcompact_wf,
rational-cube_wf,
length_wf,
less_than_wf,
rational-cube-complex_wf,
nat_wf,
subtype_rel_self,
rat-cube-complex-polyhedron-compact
Rules used in proof :
inhabitedIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
axiomEquality,
dependent_set_memberEquality_alt,
setIsType,
functionIsType,
isectIsType,
equalitySymmetry,
equalityTransitivity,
universeIsType,
lambdaEquality_alt,
independent_isectElimination,
because_Cache,
natural_numberEquality,
hypothesisEquality,
setEquality,
isectEquality,
functionEquality,
isectElimination,
sqequalHypSubstitution,
hypothesis,
extract_by_obid,
instantiate,
applyEquality,
sqequalRule,
rename,
thin,
setElimination,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k,n:\mBbbN{}]. \mforall{}[K:\{K:n-dim-complex| 0 < ||K||\} ]. (rccp-compact(k;K) \mmember{} mcompact(|K|;rn-prod-metric(k)))
Date html generated:
2019_10_31-AM-06_04_09
Last ObjectModification:
2019_10_30-PM-04_16_51
Theory : real!vectors
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