Nuprl Lemma : not-bl-exists-eq-bl-all
∀[L,P:Top]. (¬b(∃x∈L.P[x])_b ~ (∀x∈L.¬bP[x])_b)
Proof
Definitions occuring in Statement :
bl-exists: (∃x∈L.P[x])_b,
bl-all: (∀x∈L.P[x])_b,
bnot: ¬bb,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bl-all: (∀x∈L.P[x])_b,
bl-exists: (∃x∈L.P[x])_b,
reduce: reduce(f;k;as),
list_ind: list_ind,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
so_lambda: λ2x.t[x],
so_apply: x[s],
decidable: Dec(P),
or: P ∨ Q,
nat_plus: ℕ+,
subtype_rel: A ⊆r B,
has-value: (a)↓,
sq_type: SQType(T),
guard: {T},
uiff: uiff(P;Q),
btrue: tt,
bor: p ∨bq,
bfalse: ff,
band: p ∧b q
Lemmas referenced :
has-value-band-type,
bottom_diverge,
has-value-implies-dec-isaxiom-2,
assert_of_bnot,
eqff_to_assert,
eqtt_to_assert,
bool_subtype_base,
bool_wf,
subtype_base_sq,
bool_cases,
isl_wf,
injection-eta,
has-value-bor-type,
has-value-implies-dec-ispair-2,
union-value-type,
value-type-has-value,
top_wf,
is-exception_wf,
has-value_wf_base,
int_subtype_base,
has-value-bnot-type,
fun_exp_unroll_1,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
bottom-sqle,
strictness-decide,
strictness-apply,
fun_exp0_lemma,
base_wf,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
sqequalSqle,
fixpointLeast,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomSqleEquality,
unionElimination,
dependent_set_memberEquality,
divergentSqle,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
decideExceptionCases,
callbyvalueCallbyvalue,
callbyvalueReduce,
callbyvalueExceptionCases,
exceptionSqequal,
sqleReflexivity,
sqequalAxiom,
unionEquality,
instantiate,
cumulativity,
productElimination
Latex:
\mforall{}[L,P:Top]. (\mneg{}\msubb{}(\mexists{}x\mmember{}L.P[x])\_b \msim{} (\mforall{}x\mmember{}L.\mneg{}\msubb{}P[x])\_b)
Date html generated:
2016_05_14-PM-02_11_22
Last ObjectModification:
2016_01_15-AM-08_03_46
Theory : list_1
Home
Index