Nuprl Lemma : mem_append
∀s:DSet. ∀as,bs:|s| List. ∀c:|s|. c ∈b (as @ bs) = (c ∈b as) ∨b(c ∈b bs)
Proof
Definitions occuring in Statement :
mem: a ∈b as,
append: as @ bs,
list: T List,
bor: p ∨bq,
bool: 𝔹,
all: ∀x:A. B[x],
equal: s = t ∈ T,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
dset: DSet,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
prop: ℙ,
gt: i > j,
or: P ∨ Q,
uiff: uiff(P;Q),
true: True,
decidable: Dec(P),
false: False,
less_than: a < b,
squash: ↓T,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
ge: i ≥ j ,
le: A ≤ B,
subtype_rel: A ⊆r B,
guard: {T}
Lemmas referenced :
iff_imp_equal_bool,
mem_wf,
append_wf,
set_car_wf,
bor_wf,
mem_iff_count_nzero,
assert_wf,
gt_wf,
count_wf,
iff_wf,
or_wf,
assert_of_bor,
list_wf,
dset_wf,
decidable__or,
less_than_wf,
decidable__lt,
add-is-int-iff,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformor_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_or_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_wf,
false_wf,
non_neg_length,
count_bounds,
intformle_wf,
int_formula_prop_le_lemma,
squash_wf,
true_wf,
count_append,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
setElimination,
rename,
hypothesis,
independent_isectElimination,
addLevel,
productElimination,
independent_pairFormation,
impliesFunctionality,
because_Cache,
independent_functionElimination,
orFunctionality,
natural_numberEquality,
orLevelFunctionality,
unionElimination,
pointwiseFunctionality,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
imageElimination,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
approximateComputation,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
addEquality,
applyEquality,
universeEquality,
imageMemberEquality,
instantiate
Latex:
\mforall{}s:DSet. \mforall{}as,bs:|s| List. \mforall{}c:|s|. c \mmember{}\msubb{} (as @ bs) = (c \mmember{}\msubb{} as) \mvee{}\msubb{}(c \mmember{}\msubb{} bs)
Date html generated:
2018_05_22-AM-07_45_26
Last ObjectModification:
2018_05_19-AM-08_32_41
Theory : list_2
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