Nuprl Lemma : member-graph-rcvs

S:Id List. ∀G:Graph(S). ∀a:Id ─→ Id ─→ Id. ∀b:Id. ∀j:{j:Id| (j ∈ S)} . ∀k:Knd.
  ((k ∈ graph-rcvs(S;G;a;b;j)) ⇐⇒ ∃i:Id. ((i ∈ S) ∧ (i─→j)∈G ∧ (k rcv((link(a j) from to j),b) ∈ Knd)))


Definitions occuring in Statement :  graph-rcvs: graph-rcvs(S;G;a;b;j) rcv: rcv(l,tg) Knd: Knd mk_lnk: (link(n) from to j) id-graph-edge: (i─→j)∈G id-graph: Graph(S) Id: Id l_member: (x ∈ l) list: List all: x:A. B[x] exists: x:A. B[x] iff: ⇐⇒ Q and: P ∧ Q set: {x:A| B[x]}  apply: a function: x:A ─→ B[x] equal: t ∈ T
Lemmas :  list-subtype l_member-settype l_member_wf subtype_rel_list Id_wf Knd_wf rcv_wf mk_lnk_wf exists_wf assert_wf deq-member_wf id-deq_wf subtype_rel-deq sq_stable__l_member decidable__equal_Id equal_wf set_wf assert-deq-member member_map_filter mapfilter_wf iff_wf id-graph_wf list_wf
\mforall{}S:Id  List.  \mforall{}G:Graph(S).  \mforall{}a:Id  {}\mrightarrow{}  Id  {}\mrightarrow{}  Id.  \mforall{}b:Id.  \mforall{}j:\{j:Id|  (j  \mmember{}  S)\}  .  \mforall{}k:Knd.
    ((k  \mmember{}  graph-rcvs(S;G;a;b;j))
    \mLeftarrow{}{}\mRightarrow{}  \mexists{}i:Id.  ((i  \mmember{}  S)  \mwedge{}  (i{}\mrightarrow{}j)\mmember{}G  \mwedge{}  (k  =  rcv((link(a  i  j)  from  i  to  j),b))))

Date html generated: 2015_07_17-AM-09_13_36
Last ObjectModification: 2015_01_28-AM-07_58_21

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