Nuprl Lemma : bsublist_append_diff
∀s:DSet. ∀as,bs:|s| List. ((↑bsublist(s;as;bs)) ⇒ (∃cs:|s| List. ((cs @ as) ≡(|s|) bs)))
Proof
Definitions occuring in Statement :
bsublist: bsublist(s;as;bs),
permr: as ≡(T) bs,
append: as @ bs,
list: T List,
assert: ↑b,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
dset: DSet,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff
Lemmas referenced :
diff_wf,
permr_wf,
set_car_wf,
append_wf,
assert_wf,
bsublist_wf,
list_wf,
dset_wf,
permr_iff_eq_counts,
count_wf,
ndiff_wf,
equal_wf,
squash_wf,
true_wf,
count_append,
add_functionality_wrt_eq,
count_diff,
iff_weakening_equal,
count_bsublist,
le_int_wf,
bool_wf,
equal-wf-T-base,
le_wf,
decidable__equal_int,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
lt_int_wf,
less_than_wf,
bnot_wf,
ndiff_add_eq_imax,
imax_unfold,
uiff_transitivity,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
dependent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
isectElimination,
setElimination,
rename,
because_Cache,
productElimination,
independent_functionElimination,
intEquality,
natural_numberEquality,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
independent_isectElimination,
unionElimination,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
equalityElimination
Latex:
\mforall{}s:DSet. \mforall{}as,bs:|s| List. ((\muparrow{}bsublist(s;as;bs)) {}\mRightarrow{} (\mexists{}cs:|s| List. ((cs @ as) \mequiv{}(|s|) bs)))
Date html generated:
2017_10_01-AM-09_57_21
Last ObjectModification:
2017_03_03-PM-00_58_53
Theory : list_2
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