Nuprl Lemma : OARcast_SenderState-classrel
∀[M:ValueAllType]. ∀[deliverhdr,oarcasthdr,orderedhdr,orderhdr:Atom List].
∀[mf:OARcast_headers_type{i:l}(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr)].
∀es:EO+(Message(mf)). ∀e:E. ∀v:ℤ.
(v ∈ OARcast_SenderState(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr;mf)(e)
⇐⇒ v = OARcast_SenderStateFun(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr;mf;es;e) ∈ ℤ)
Proof
Definitions occuring in Statement :
OARcast_SenderStateFun: OARcast_SenderStateFun(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr;mf;es;e),
OARcast_SenderState: OARcast_SenderState(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr;mf),
OARcast_headers_type: OARcast_headers_type{i:l}(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-E: E,
list: T List,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
int: ℤ,
atom: Atom,
equal: s = t ∈ T
Lemmas :
sq_stable__and,
equal_wf,
vatype_wf,
Id_wf,
sq_stable__equal,
squash_wf,
int_seg_wf,
length_wf,
name_wf,
OARcast_headers_wf,
l_all_iff,
l_member_wf,
OARcast_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,
classrel-classfun,
OARcast_SenderState-functional,
classrel_wf,
OARcast_SenderState_wf,
equal-wf-base-T,
int_subtype_base,
OARcast_SenderStateFun_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
Message_wf,
subtype_rel_dep_function,
OARcast_headers_type_wf,
list_wf,
set_wf,
valueall-type_wf
Latex:
\mforall{}[M:ValueAllType]. \mforall{}[deliverhdr,oarcasthdr,orderedhdr,orderhdr:Atom List].
\mforall{}[mf:OARcast\_headers\_type\{i:l\}(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr)].
\mforall{}es:EO+(Message(mf)). \mforall{}e:E. \mforall{}v:\mBbbZ{}.
(v \mmember{} OARcast\_SenderState(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr;mf)(e)
\mLeftarrow{}{}\mRightarrow{} v = OARcast\_SenderStateFun(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr;mf;es;e))
Date html generated:
2015_07_23-PM-00_30_37
Last ObjectModification:
2015_02_04-PM-02_54_34
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