Nuprl Lemma : rat-cube-complex-polyhedron-inhabited
∀k:ℕ. ∀[n:ℕ]. ∀K:n-dim-complex. (0 < ||K|| ⇒ |K|)
Proof
Definitions occuring in Statement :
rat-cube-complex-polyhedron: |K|,
length: ||as||,
nat: ℕ,
less_than: a < b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n,
rational-cube-complex: n-dim-complex
Definitions unfolded in proof :
le: A ≤ B,
stable-union: Error :stable-union,
rat-cube-complex-polyhedron: |K|,
rev_implies: P ⇐ Q,
bfalse: ff,
iff: P ⇐⇒ Q,
btrue: tt,
ifthenelse: if b then t else f fi ,
guard: {T},
sq_type: SQType(T),
rat-cube-dimension: dim(c),
select: L[n],
uiff: uiff(P;Q),
prop: ℙ,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
uimplies: b supposing a,
decidable: Dec(P),
lelt: i ≤ j < k,
ge: i ≥ j ,
nat: ℕ,
int_seg: {i..j-},
l_all: (∀x∈L.P[x]),
top: Top,
cons: [a / b],
and: P ∧ Q,
false: False,
less_than': less_than'(a;b),
squash: ↓T,
less_than: a < b,
or: P ∨ Q,
member: t ∈ T,
rational-cube-complex: n-dim-complex,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
int_seg_wf,
non_neg_length,
int_seg_properties,
cons_wf,
select_wf,
in-rat-cube_wf,
istype-false,
select-cons-hd,
int_formula_prop_eq_lemma,
intformeq_wf,
assert_of_bnot,
eqff_to_assert,
inhabited-iff-in-rat-cube,
eqtt_to_assert,
bool_subtype_base,
bool_wf,
subtype_base_sq,
bool_cases,
inhabited-rat-cube_wf,
false_wf,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
itermAdd_wf,
intformless_wf,
add-is-int-iff,
istype-le,
int_term_value_var_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
intformand_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
istype-int,
itermConstant_wf,
intformle_wf,
intformnot_wf,
full-omega-unsat,
decidable__le,
nat_properties,
istype-nat,
rational-cube-complex_wf,
length_wf,
istype-less_than,
istype-void,
length_of_cons_lemma,
product_subtype_list,
length_of_nil_lemma,
list-cases,
rational-cube_wf
Rules used in proof :
functionIsType,
because_Cache,
minusEquality,
cumulativity,
instantiate,
productIsType,
baseClosed,
closedConclusion,
baseApply,
equalitySymmetry,
equalityTransitivity,
pointwiseFunctionality,
int_eqEquality,
addEquality,
lambdaEquality_alt,
dependent_pairFormation_alt,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
independent_pairFormation,
dependent_set_memberEquality_alt,
inhabitedIsType,
universeIsType,
natural_numberEquality,
isect_memberEquality_alt,
hypothesis_subsumption,
promote_hyp,
voidElimination,
productElimination,
imageElimination,
sqequalRule,
unionElimination,
dependent_functionElimination,
hypothesis,
hypothesisEquality,
isectElimination,
extract_by_obid,
introduction,
cut,
rename,
thin,
setElimination,
sqequalHypSubstitution,
isect_memberFormation_alt,
lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}k:\mBbbN{}. \mforall{}[n:\mBbbN{}]. \mforall{}K:n-dim-complex. (0 < ||K|| {}\mRightarrow{} |K|)
Date html generated:
2019_10_30-AM-10_13_13
Last ObjectModification:
2019_10_26-PM-00_49_53
Theory : real!vectors
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