Nuprl Lemma : bl-exists-append
∀[L1,L2,P:Top]. ((∃x∈L1 @ L2.P[x])_b ~ (∃x∈L1.P[x])_b ∨b(∃x∈L2.P[x])_b)
Proof
Definitions occuring in Statement :
bl-exists: (∃x∈L.P[x])_b,
append: as @ bs,
bor: p ∨bq,
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-exists: (∃x∈L.P[x])_b,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
reduce: reduce(f;k;as),
list_ind: list_ind,
nat: ℕ,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
and: P ∧ Q,
prop: ℙ,
bor: p ∨bq,
ifthenelse: if b then t else f fi ,
decidable: Dec(P),
or: P ∨ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
compose: f o g,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
strict4: strict4(F),
has-value: (a)↓,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
reduce-append,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
top_wf,
fun_exp0_lemma,
strictness-apply,
bottom-sqle,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
fun_exp_unroll,
le_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
intformeq_wf,
int_formula_prop_eq_lemma,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
strictness-decide,
lifting-strict-callbyvalue,
has-value_wf_base,
base_wf,
is-exception_wf,
lifting-strict-ispair,
lifting-strict-spread,
lifting-strict-decide,
lifting-strict-isaxiom,
bor_assoc
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
hypothesis,
because_Cache,
lambdaFormation,
sqequalSqle,
fixpointLeast,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomSqleEquality,
unionElimination,
dependent_set_memberEquality,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
promote_hyp,
instantiate,
cumulativity,
sqequalAxiom,
baseClosed,
callbyvalueDecide,
unionEquality,
sqleReflexivity,
baseApply,
closedConclusion,
decideExceptionCases,
inrFormation,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation,
sqleRule,
divergentSqle
Latex:
\mforall{}[L1,L2,P:Top]. ((\mexists{}x\mmember{}L1 @ L2.P[x])\_b \msim{} (\mexists{}x\mmember{}L1.P[x])\_b \mvee{}\msubb{}(\mexists{}x\mmember{}L2.P[x])\_b)
Date html generated:
2017_04_17-AM-08_03_43
Last ObjectModification:
2017_02_27-PM-04_34_13
Theory : list_1
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