Nuprl Lemma : mFOL-bound-rename
This lemma shows that there is a formula
with the same abstract meaning whose bound variables are disjoint from
a given list of variables.⋅
∀fmla:mFOL(). ∀L:ℤ List.
(∃fmla':{mFOL()| ((mFOL-abstract(fmla') = mFOL-abstract(fmla) ∈ AbstractFOFormula)
∧ l_disjoint(ℤ;L;mFOL-boundvars(fmla')))})
Proof
Definitions occuring in Statement :
mFOL-abstract: mFOL-abstract(fmla),
mFOL-boundvars: mFOL-boundvars(fmla),
mFOL: mFOL(),
AbstractFOFormula: AbstractFOFormula,
l_disjoint: l_disjoint(T;l1;l2),
list: T List,
all: ∀x:A. B[x],
sq_exists: ∃x:{A| B[x]},
and: P ∧ Q,
int: ℤ,
equal: s = t ∈ T
Lemmas :
mFOL-induction,
all_wf,
list_wf,
sq_exists_wf,
mFOL_wf,
AbstractFOFormula_wf,
mFOL-abstract_wf,
l_disjoint_wf,
mFOL-boundvars_wf,
bool_wf,
atom_subtype_base,
int_subtype_base,
list_subtype_base,
equal-wf-T-base,
l_disjoint_nil2,
mFOatomic_wf,
mFOconnect_wf,
squash_wf,
l_member_wf,
decidable__equal_int,
decidable__l_disjoint,
sq_stable_from_decidable,
sq_stable__equal,
equal_wf,
sq_stable__and,
iff_weakening_equal,
FOConnective_wf,
int-deq_wf,
l-union_wf,
member-union,
decidable__l_member,
append_wf,
mFOL-freevars_wf,
list-cases,
null_nil_lemma,
product_subtype_list,
null_cons_lemma,
imax-list_wf,
cons_wf,
length_wf,
non_neg_length,
length_wf_nat,
length_cons,
not_wf,
equal-wf-base,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
eqff_to_assert,
btrue_neq_bfalse,
and_wf,
member-implies-null-eq-bfalse,
btrue_wf,
assert_of_null,
eqtt_to_assert,
top_wf,
subtype_rel_list,
null_wf3,
length_of_nil_lemma,
nil_wf,
length_of_cons_lemma,
nat_wf,
decidable__lt,
false_wf,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
imax-list-lb,
le_weakening,
lelt_wf,
le_antisymmetry_iff,
add-swap,
member_append,
or_wf,
mFOquant_wf,
mFOL-rename_wf,
FOAssignment_wf,
FOStruct_wf,
FOSatWith_wf,
update-assignment_wf,
mFOL-abstract-rename,
eq_int_wf,
assert_of_eq_int,
neg_assert_of_eq_int,
mFOL-abstract-functionality,
ite_rw_false,
assert_wf,
exists_wf,
true_wf,
insert_wf,
deq_wf,
mFOL-boundvars-of-rename,
member-insert,
FOQuantifier_wf
\mforall{}fmla:mFOL(). \mforall{}L:\mBbbZ{} List.
(\mexists{}fmla':\{mFOL()| ((mFOL-abstract(fmla') = mFOL-abstract(fmla))
\mwedge{} l\_disjoint(\mBbbZ{};L;mFOL-boundvars(fmla')))\})
Date html generated:
2015_07_17-AM-07_54_35
Last ObjectModification:
2015_07_15-PM-04_25_13
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