Nuprl Lemma : ncomplete-test
((∀a:Prop. (localT prop(a) ∈ Prop List)) ∧ (∀n:node. (fst(n) ∈ Prop List)))
∧ (∀n:node. (∀f∈fst(n).f ∈ Prop))
∧ (∀n:node. (∀f1∈fst(n).(∀f∈localT prop(f1).f ∈ Prop)))
∧ (∀n:node. (∀f∈fst(n).(∀f1∈localT prop(f).(∃f1'∈fst(n). dlo_eq(prop(f1);prop(f1')) ∈ 𝔹))))
Proof
Definitions occuring in Statement : 
dl-localT: localT
, 
node: node
, 
dlo_eq: dlo_eq(a;b)
, 
dl-prop-obj: prop(x)
, 
dl-prop: Prop
, 
l_exists: (∃x∈L. P[x])
, 
l_all: (∀x∈L.P[x])
, 
list: T List
, 
bool: 𝔹
, 
pi1: fst(t)
, 
all: ∀x:A. B[x]
, 
and: P ∧ Q
, 
member: t ∈ T
, 
apply: f a
Definitions unfolded in proof : 
and: P ∧ Q
, 
cand: A c∧ B
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
node: node
, 
top: Top
, 
l_all: (∀x∈L.P[x])
, 
pi1: fst(t)
, 
int_seg: {i..j-}
, 
uimplies: b supposing a
, 
lelt: i ≤ j < k
, 
le: A ≤ B
, 
less_than: a < b
, 
squash: ↓T
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
prop: ℙ
, 
guard: {T}
, 
l_exists: (∃x∈L. P[x])
Lemmas referenced : 
dl-localT_wf, 
dl-prop-obj_wf, 
dl-prop_wf, 
pi1_wf_top, 
list_wf, 
istype-void, 
node_wf, 
select_wf, 
int_seg_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, 
decidable__lt, 
length_wf, 
intformless_wf, 
int_formula_prop_less_lemma, 
int_seg_wf, 
dlo_eq_wf, 
bool_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
cut, 
lambdaFormation_alt, 
applyEquality, 
introduction, 
extract_by_obid, 
hypothesis, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
hypothesisEquality, 
universeIsType, 
independent_pairFormation, 
isectElimination, 
productElimination, 
independent_pairEquality, 
isect_memberEquality_alt, 
voidElimination, 
because_Cache, 
sqequalRule, 
setElimination, 
rename, 
independent_isectElimination, 
imageElimination, 
natural_numberEquality, 
unionElimination, 
approximateComputation, 
independent_functionElimination, 
dependent_pairFormation_alt, 
lambdaEquality_alt, 
int_eqEquality, 
equalityIstype
Latex:
((\mforall{}a:Prop.  (localT  prop(a)  \mmember{}  Prop  List))  \mwedge{}  (\mforall{}n:node.  (fst(n)  \mmember{}  Prop  List)))
\mwedge{}  (\mforall{}n:node.  (\mforall{}f\mmember{}fst(n).f  \mmember{}  Prop))
\mwedge{}  (\mforall{}n:node.  (\mforall{}f1\mmember{}fst(n).(\mforall{}f\mmember{}localT  prop(f1).f  \mmember{}  Prop)))
\mwedge{}  (\mforall{}n:node.  (\mforall{}f\mmember{}fst(n).(\mforall{}f1\mmember{}localT  prop(f).(\mexists{}f1'\mmember{}fst(n).  dlo\_eq(prop(f1);prop(f1'))  \mmember{}  \mBbbB{}))))
Date html generated:
2020_05_20-AM-09_02_13
Last ObjectModification:
2019_11_27-PM-02_31_18
Theory : dynamic!logic
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