Nuprl Lemma : nysiad_MessageBagState-classrel
∀[M:ValueAllType]. ∀[add2baghdr,addwaitinghdr,adeliverhdr:Atom List]. ∀[deqM:EqDecider(M)].
∀[inputmsghdr,kdeliverhdr,readyhdr,tooarcasthdr:Atom List]. ∀[waitingmap:map-sig{i:l}(Id;M)].
∀[mf:nysiad_headers_type{i:l}(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr)].
∀[msg2m:Message(mf) ─→ M].
∀es:EO+(Message(mf)). ∀e:E. ∀v:(M × Id? × Id) List × map-sig-map(waitingmap).
(v ∈
nysiad_MessageBagState(M;add2baghdr;addwaitinghdr;adeliverhdr;deqM;inputmsghdr;kdeliverhdr;...;...;...;mf;msg2m)(
e)
⇐⇒ v
= nysiad_MessageBagStateFun(M;add2baghdr;addwaitinghdr;adeliverhdr;deqM;inputmsghdr;...;...;...;...;mf;...;es;e)
∈ ((M × Id? × Id) List × map-sig-map(waitingmap)))
Proof
Definitions occuring in Statement :
nysiad_MessageBagStateFun: nysiad_MessageBagStateFun(M;add2baghdr;addwaitinghdr;adeliverhdr;deqM;inputmsghdr;kdeliverhdr;...;...;...;mf;msg2m;es;e),
nysiad_MessageBagState: nysiad_MessageBagState(M;add2baghdr;addwaitinghdr;adeliverhdr;deqM;inputmsghdr;kdeliverhdr;readyhdr;...;...;mf;msg2m),
nysiad_headers_type: nysiad_headers_type{i:l}(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
deq: EqDecider(T),
list: T List,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
unit: Unit,
function: x:A ─→ B[x],
product: x:A × B[x],
union: left + right,
atom: Atom,
equal: s = t ∈ T,
map-sig-map: map-sig-map(m),
map-sig: map-sig{i:l}(Key;Value)
Lemmas :
sq_stable__and,
equal_wf,
vatype_wf,
equal-wf-T-base,
sq_stable__equal,
squash_wf,
int_seg_wf,
length_wf,
name_wf,
nysiad_headers_wf,
l_all_iff,
l_member_wf,
nysiad_headers_fun_wf,
cons_member,
cons_wf,
nil_wf,
equal-wf-base,
list_subtype_base,
atom_subtype_base,
iff_weakening_equal,
name_eq_wf,
bool_wf,
eqtt_to_assert,
assert-name_eq,
sq_stable__no_repeats,
true_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
Message_wf,
subtype_rel_dep_function,
Id_wf,
unit_wf2,
classrel-classfun,
nysiad_MessageBagState-functional,
classrel_wf,
list_wf,
map-sig-map_wf,
nysiad_MessageBagState_wf,
nysiad_MessageBagStateFun_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
nysiad_headers_type_wf,
map-sig_wf,
deq_wf,
set_wf,
valueall-type_wf
Latex:
\mforall{}[M:ValueAllType]. \mforall{}[add2baghdr,addwaitinghdr,adeliverhdr:Atom List]. \mforall{}[deqM:EqDecider(M)].
\mforall{}[inputmsghdr,kdeliverhdr,readyhdr,tooarcasthdr:Atom List]. \mforall{}[waitingmap:map-sig\{i:l\}(Id;M)].
\mforall{}[...
Date html generated:
2015_07_23-PM-03_43_46
Last ObjectModification:
2015_02_04-PM-04_24_24
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