Nuprl Lemma : mFOL-abstract-functionality
∀[fmla:mFOL()]. ∀[Dom:Type]. ∀[S:FOStruct(Dom)]. ∀[a1,a2:FOAssignment(Dom)].
Dom,S,a1 |= mFOL-abstract(fmla) = Dom,S,a2 |= mFOL-abstract(fmla) ∈ ℙ
supposing ∀z:ℤ. ((z ∈ mFOL-freevars(fmla)) ⇒ ((a1 z) = (a2 z) ∈ Dom))
Proof
Definitions occuring in Statement :
mFOL-abstract: mFOL-abstract(fmla),
mFOL-freevars: mFOL-freevars(fmla),
mFOL: mFOL(),
FOSatWith: Dom,S,a |= fmla,
FOStruct: FOStruct(Dom),
FOAssignment: FOAssignment(Dom),
l_member: (x ∈ l),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Lemmas :
mFOL-induction,
all_wf,
FOAssignment_wf,
l_member_wf,
mFOL-freevars_wf,
FOSatWith_wf,
mFOL-abstract_wf,
mFOL_wf,
mFOatomic_wf,
list_wf,
mFOconnect_wf,
mFOquant_wf,
bool_wf,
FOStruct_wf,
member-remove-repeats,
int-deq_wf,
list_induction,
map_wf,
map_nil_lemma,
nil_wf,
map_cons_lemma,
cons_wf,
squash_wf,
true_wf,
cons_member,
equal_wf,
iff_weakening_equal,
eq_atom_wf,
eqtt_to_assert,
assert_of_eq_atom,
and_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
or_wf,
int-valueall-type,
val-union-l-union,
member-union,
update-assignment_wf,
eq_int_wf,
assert_of_eq_int,
neg_assert_of_eq_int,
member_filter,
bnot_wf,
iff_transitivity,
assert_wf,
not_wf,
equal-wf-base,
int_subtype_base,
iff_weakening_uiff,
assert_of_bnot,
exists_wf
\mforall{}[fmla:mFOL()]. \mforall{}[Dom:Type]. \mforall{}[S:FOStruct(Dom)]. \mforall{}[a1,a2:FOAssignment(Dom)].
Dom,S,a1 |= mFOL-abstract(fmla) = Dom,S,a2 |= mFOL-abstract(fmla)
supposing \mforall{}z:\mBbbZ{}. ((z \mmember{} mFOL-freevars(fmla)) {}\mRightarrow{} ((a1 z) = (a2 z)))
Date html generated:
2015_07_17-AM-07_54_27
Last ObjectModification:
2015_02_03-PM-09_38_54
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