Nuprl Lemma : loop-class-memory-eq
∀[Info,B:Type]. ∀[X:EClass(B ─→ B)]. ∀[init:Id ─→ bag(B)]. ∀[es:EO+(Info)]. ∀[e:E].
(loop-class-memory(X;init)(e)
= if first(e) then init loc(e)
if pred(e) ∈b X then eclass3(X;loop-class-memory(X;init))(pred(e))
else loop-class-memory(X;init)(pred(e))
fi
∈ bag(B))
Proof
Definitions occuring in Statement :
loop-class-memory: loop-class-memory(X;init),
eclass3: eclass3(X;Y),
member-eclass: e ∈b X,
class-ap: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-loc: loc(e),
es-E: E,
Id: Id,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Lemmas :
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
int_seg_wf,
int_seg_subtype-nat,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
eqtt_to_assert,
eqff_to_assert,
equal_wf,
bool_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
Id_wf,
bag_wf,
eclass_wf,
es-local-pred_wf,
lt_int_wf,
bag-size_wf,
class-ap_wf,
eclass3_wf,
loop-class-memory_wf,
or_wf,
sq_exists_wf,
es-locl_wf,
assert_wf,
all_wf,
not_wf,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
es-loc_wf,
member-eclass_wf,
es-pred_wf,
loop-class-memory-no-input,
es-first_wf2,
iff_weakening_equal,
loop-class-memory-prior-eq,
es-pred_property,
es-pred-locl,
es-causl_weakening,
es-loc-pred,
assert_of_lt_int,
bag-member-iff-size,
loop-class-memory-exists,
assert-member-eclass,
eclass3-classrel,
classrel_wf,
exists_wf,
equal-wf-T-base,
loop-class-memory-size-zero,
bag-size-is-zero,
bag_map_empty_lemma,
empty-bag_wf,
bag-combine-empty-right,
es-pred-loc-base,
bag-member_wf,
bag-size-zero,
assert-bag-null,
null-bag-size,
assert_of_eq_int
Latex:
\mforall{}[Info,B:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} B)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
(loop-class-memory(X;init)(e)
= if first(e) then init loc(e)
if pred(e) \mmember{}\msubb{} X then eclass3(X;loop-class-memory(X;init))(pred(e))
else loop-class-memory(X;init)(pred(e))
fi )
Date html generated:
2015_07_21-PM-02_36_21
Last ObjectModification:
2015_02_04-PM-06_21_33
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