Nuprl Lemma : rat-cube-complex-polyhedron-compact
∀k:ℕ. ∀[n:ℕ]. ∀K:{K:n-dim-complex| 0 < ||K||} . mcompact(|K|;rn-prod-metric(k))
Proof
Definitions occuring in Statement :
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],
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
natural_number: $n,
rational-cube-complex: n-dim-complex
Definitions unfolded in proof :
bfalse: ff,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
guard: {T},
sq_type: SQType(T),
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
nat: ℕ,
squash: ↓T,
less_than: a < b,
le: A ≤ B,
lelt: i ≤ j < k,
uimplies: b supposing a,
int_seg: {i..j-},
rat-cube-dimension: dim(c),
l_all: (∀x∈L.P[x]),
and: P ∧ Q,
sq_stable: SqStable(P),
implies: P ⇒ Q,
so_apply: x[s],
prop: ℙ,
so_lambda: λ2x.t[x],
member: t ∈ T,
rational-cube-complex: n-dim-complex,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
istype-nat,
istype-less_than,
rational-cube-complex_wf,
rat-cube-complex-polyhedron-compact1,
int_seg_wf,
int_formula_prop_eq_lemma,
intformeq_wf,
assert_of_bnot,
eqff_to_assert,
eqtt_to_assert,
bool_subtype_base,
bool_wf,
subtype_base_sq,
bool_cases,
int_formula_prop_less_lemma,
intformless_wf,
istype-le,
length_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_and_lemma,
istype-int,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
nat_properties,
int_seg_properties,
select_wf,
assert_witness,
sq_stable__assert,
l_member_wf,
inhabited-rat-cube_wf,
assert_wf,
rational-cube_wf,
sq_stable__l_all
Rules used in proof :
baseClosed,
imageMemberEquality,
minusEquality,
equalitySymmetry,
equalityTransitivity,
cumulativity,
instantiate,
dependent_set_memberEquality_alt,
independent_pairFormation,
voidElimination,
isect_memberEquality_alt,
int_eqEquality,
dependent_pairFormation_alt,
approximateComputation,
unionElimination,
natural_numberEquality,
imageElimination,
independent_isectElimination,
productElimination,
inhabitedIsType,
functionIsTypeImplies,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
universeIsType,
setIsType,
lambdaEquality_alt,
sqequalRule,
hypothesis,
hypothesisEquality,
isectElimination,
extract_by_obid,
introduction,
sqequalHypSubstitution,
rename,
thin,
setElimination,
cut,
isect_memberFormation_alt,
lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}k:\mBbbN{}. \mforall{}[n:\mBbbN{}]. \mforall{}K:\{K:n-dim-complex| 0 < ||K||\} . mcompact(|K|;rn-prod-metric(k))
Date html generated:
2019_10_31-AM-06_04_02
Last ObjectModification:
2019_10_30-PM-04_14_39
Theory : real!vectors
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