Nuprl Lemma : rat-complex-subdiv-non-nil
∀[k,n:ℕ]. ∀[K:n-dim-complex]. 0 < ||(K)'|| supposing 0 < ||K||
Proof
Definitions occuring in Statement :
rat-complex-subdiv: (K)',
rational-cube-complex: n-dim-complex,
length: ||as||,
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
rational-cube-complex: n-dim-complex,
all: ∀x:A. B[x],
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
false: False,
and: P ∧ Q,
cons: [a / b],
top: Top,
exists: ∃x:A. B[x],
cand: A c∧ B,
l_member: (x ∈ l),
nat: ℕ,
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
select: L[n],
ge: i ≥ j ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
prop: ℙ,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
true: True,
guard: {T},
nat_plus: ℕ+,
uiff: uiff(P;Q),
rational-cube: ℚCube(k),
rational-interval: ℚInterval,
rev_uimplies: rev_uimplies(P;Q),
is-half-interval: is-half-interval(I;J),
sq_type: SQType(T),
bfalse: ff,
band: p ∧b q,
ifthenelse: if b then t else f fi
Lemmas referenced :
member_not_nil,
rational-cube_wf,
rat-complex-subdiv_wf,
list-cases,
length_of_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
istype-void,
istype-le,
cons_wf,
istype-less_than,
length_wf,
select_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
l_member_wf,
istype-assert,
is-half-cube_wf,
member-rat-complex-subdiv2,
less_than_wf,
squash_wf,
true_wf,
length_of_null_list,
nil_wf,
subtype_rel_self,
iff_weakening_equal,
add_nat_plus,
length_wf_nat,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
nat_plus_properties,
add-is-int-iff,
itermAdd_wf,
intformeq_wf,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
false_wf,
list_wf,
member-less_than,
rational-cube-complex_wf,
istype-nat,
qavg_wf,
int_seg_wf,
assert-is-half-cube,
assert_wf,
bor_wf,
qeq_wf2,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
band_wf,
btrue_wf,
assert-qeq,
bfalse_wf,
member_wf,
rationals_wf,
equal_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_bor,
assert_of_band
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality_alt,
setElimination,
rename,
because_Cache,
sqequalRule,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
imageElimination,
productElimination,
voidElimination,
promote_hyp,
hypothesis_subsumption,
isect_memberEquality_alt,
dependent_pairFormation_alt,
dependent_set_memberEquality_alt,
natural_numberEquality,
independent_pairFormation,
lambdaFormation_alt,
inhabitedIsType,
productIsType,
equalityIstype,
approximateComputation,
independent_functionElimination,
int_eqEquality,
universeIsType,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed,
instantiate,
universeEquality,
applyLambdaEquality,
pointwiseFunctionality,
baseApply,
closedConclusion,
functionIsType,
isectIsTypeImplies,
independent_pairEquality,
cumulativity,
unionEquality,
productEquality,
unionIsType,
inlFormation_alt,
inrFormation_alt
Latex:
\mforall{}[k,n:\mBbbN{}]. \mforall{}[K:n-dim-complex]. 0 < ||(K)'|| supposing 0 < ||K||
Date html generated:
2020_05_20-AM-09_23_32
Last ObjectModification:
2019_10_31-AM-00_58_04
Theory : rationals
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