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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