Nuprl Lemma : rec-class-unique
∀[Info,T:Type]. ∀[G:es:EO+(Info) ─→ E ─→ bag(T)]. ∀[F:es:EO+(Info) ─→ e':E ─→ T ─→ {e:E| (e' <loc e)} ─→ bag(T)].
∀[X:EClass(T)].
X = RecClass(first e G[es;e]or next e after e' with value v F[es;e';v;e]) ∈ EClass(T)
supposing ∀es:EO+(Info). ∀e:E.
((X es e) = if e ∈b prior(X) then let e' = prior(X)(e) in F[es;e';X(e');e] else G[es;e] fi ∈ bag(T))
Proof
Definitions occuring in Statement :
es-rec-class: es-rec-class,
es-prior-interface: prior(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
ifthenelse: if b then t else f fi ,
let: let,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3;s4],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Lemmas :
all_wf,
event-ordering+_wf,
es-E_wf,
event-ordering+_subtype,
equal_wf,
bag_wf,
in-eclass_wf,
es-prior-interface_wf1,
es-interface-subtype_rel2,
top_wf,
subtype_top,
es-E-interface_wf,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
eclass_wf,
es-locl_wf,
es-rec-class_wf,
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,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
squash_wf,
true_wf,
es-prior-interface-equal,
assert_wf,
or_wf,
eq_int_wf,
bag-size_wf,
es-causl_weakening,
assert_functionality_wrt_uiff,
eclass-val_wf2,
es-prior-interface_wf,
set_wf,
subtype_rel_dep_function,
subtype_rel_sets,
event_ordering_wf,
iff_weakening_equal,
subtype_rel_self,
Id_wf,
es-loc-prior-interface,
es-loc_wf,
es-prior-interface-causl,
es-prior-interface-val,
bag-only_wf2,
single-valued-bag_wf,
assert_of_eq_int,
single-valued-bag-if-le1,
le_antisymmetry_iff,
is-prior-interface,
eclass-val_wf,
es-E-interface-property
Latex:
\mforall{}[Info,T:Type]. \mforall{}[G:es:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} bag(T)]. \mforall{}[F:es:EO+(Info)
{}\mrightarrow{} e':E
{}\mrightarrow{} T
{}\mrightarrow{} \{e:E| (e' <loc e)\}
{}\mrightarrow{} bag(T)]. \mforall{}[X:EClass(T)].
X = RecClass(first e G[es;e]or next e after e' with value v F[es;e';v;e])
supposing \mforall{}es:EO+(Info). \mforall{}e:E.
((X es e)
= if e \mmember{}\msubb{} prior(X) then let e' = prior(X)(e) in F[es;e';X(e');e] else G[es;e] fi )
Date html generated:
2015_07_21-PM-03_21_45
Last ObjectModification:
2015_02_04-PM-06_18_50
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