Nuprl Lemma : not-isl-priority-select
∀[T:Type]. ∀[as:T List]. ∀[f,g:T ⟶ 𝔹].  uiff(¬↑isl(priority-select(f;g;as));(∀a∈as.(¬↑(f a)) ∧ (¬↑(g a))))
Proof
Definitions occuring in Statement : 
priority-select: priority-select(f;g;as)
, 
l_all: (∀x∈L.P[x])
, 
list: T List
, 
assert: ↑b
, 
isl: isl(x)
, 
bool: 𝔹
, 
uiff: uiff(P;Q)
, 
uall: ∀[x:A]. B[x]
, 
not: ¬A
, 
and: P ∧ Q
, 
apply: f a
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
prop: ℙ
, 
not: ¬A
, 
false: False
, 
isl: isl(x)
, 
rev_implies: P 
⇐ Q
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
iff: P 
⇐⇒ Q
, 
l_all: (∀x∈L.P[x])
, 
int_seg: {i..j-}
, 
guard: {T}
, 
lelt: i ≤ j < k
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
top: Top
, 
less_than: a < b
, 
squash: ↓T
, 
subtype_rel: A ⊆r B
, 
assert: ↑b
, 
ifthenelse: if b then t else f fi 
, 
btrue: tt
, 
true: True
, 
bfalse: ff
Lemmas referenced : 
priority-select_wf, 
bool_wf, 
unit_wf2, 
not_wf, 
assert_wf, 
isl_wf, 
assert_elim, 
and_wf, 
equal_wf, 
bfalse_wf, 
btrue_neq_bfalse, 
equal-wf-T-base, 
iff_weakening_uiff, 
l_all_wf2, 
l_member_wf, 
priority-select-inr, 
select_wf, 
int_seg_properties, 
length_wf, 
decidable__le, 
satisfiable-full-omega-tt, 
intformand_wf, 
intformnot_wf, 
intformle_wf, 
itermConstant_wf, 
itermVar_wf, 
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, 
intformless_wf, 
int_formula_prop_less_lemma, 
int_seg_wf, 
uiff_wf, 
list_wf, 
equal-unit, 
it_wf
Rules used in proof : 
cut, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
cumulativity, 
hypothesisEquality, 
functionExtensionality, 
applyEquality, 
hypothesis, 
unionEquality, 
lambdaFormation, 
independent_pairFormation, 
isect_memberFormation, 
addLevel, 
independent_isectElimination, 
levelHypothesis, 
dependent_set_memberEquality, 
equalityTransitivity, 
equalitySymmetry, 
applyLambdaEquality, 
setElimination, 
rename, 
productElimination, 
sqequalRule, 
independent_functionElimination, 
voidElimination, 
lambdaEquality, 
dependent_functionElimination, 
because_Cache, 
productEquality, 
setEquality, 
baseClosed, 
independent_pairEquality, 
natural_numberEquality, 
unionElimination, 
dependent_pairFormation, 
int_eqEquality, 
intEquality, 
isect_memberEquality, 
voidEquality, 
computeAll, 
imageElimination, 
universeEquality, 
functionEquality, 
inrEquality
Latex:
\mforall{}[T:Type].  \mforall{}[as:T  List].  \mforall{}[f,g:T  {}\mrightarrow{}  \mBbbB{}].
    uiff(\mneg{}\muparrow{}isl(priority-select(f;g;as));(\mforall{}a\mmember{}as.(\mneg{}\muparrow{}(f  a))  \mwedge{}  (\mneg{}\muparrow{}(g  a))))
Date html generated:
2018_05_21-PM-06_49_50
Last ObjectModification:
2017_07_26-PM-04_56_55
Theory : general
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