Nuprl Lemma : es-interface-history-prior
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[X:EClass(A List)]. ∀[e:E(X)].
(es-interface-history(es;X;e)
= if e ∈b prior(X) then es-interface-history(es;X;prior(X)(e)) @ X(e) else X(e) fi
∈ (A List))
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
es-interface-history: es-interface-history(es;X;e),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
append: as @ bs,
list: T List,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
es-next,
event-ordering+_subtype,
Id_wf,
es-loc-prior-interface,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_wf,
top_wf,
subtype_top,
list_wf,
es-loc_wf,
iff_weakening_equal,
es-prior-interface-causl,
es-prior-interface_wf0,
eclass_wf,
eclass-val_wf,
assert_functionality_wrt_uiff,
in-eclass_wf,
squash_wf,
true_wf,
es-le_wf,
not_wf,
assert_wf,
es-first_wf2,
es-pred_wf,
es-le-before-partition2,
length_wf_nat,
es-le-before_wf,
equal_wf,
nat_wf,
concat_wf,
mapfilter_wf,
es-E-interface-property,
append_wf,
set_wf,
assert_elim,
subtype_base_sq,
bool_wf,
bool_subtype_base,
mapfilter-append,
concat_append,
map_cons_lemma,
map_nil_lemma,
concat-single,
subtype_rel_list,
map_wf,
es-E-interface_wf,
es-le-self,
es-interval-partition,
filter_append,
es-interval_wf,
es-locl-first,
btrue_neq_bfalse,
filter_is_nil,
l_all_iff,
l_member_wf,
member-es-interval,
es-prior-interface_wf,
es-prior-interface-val,
es-pred-locl,
es-locl_transitivity1,
es-le_weakening_eq,
es-locl_transitivity2,
eclass-val_wf2,
list_ind_nil_lemma,
es-interval-eq,
filter_cons_lemma,
filter_nil_lemma,
eqtt_to_assert,
cons_wf,
nil_wf,
eqff_to_assert,
bool_cases_sqequal,
assert-bnot,
not_assert_elim,
es-interface-sublist_wf,
es-interval-eq2,
es-before_wf,
reduce_nil_lemma,
member-es-before,
es-is-prior-interface,
es-locl_wf,
reduce_cons_lemma,
append_back_nil,
equal-wf-T-base,
bnot_wf,
uiff_transitivity,
assert_of_bnot
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X:EClass(A List)]. \mforall{}[e:E(X)].
(es-interface-history(es;X;e)
= if e \mmember{}\msubb{} prior(X) then es-interface-history(es;X;prior(X)(e)) @ X(e) else X(e) fi )
Date html generated:
2015_07_21-PM-03_31_58
Last ObjectModification:
2015_02_04-PM-06_15_59
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