### 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 i j) from i to j),b) ∈ Knd)))`

Proof

Definitions occuring in Statement :  graph-rcvs: `graph-rcvs(S;G;a;b;j)` rcv: `rcv(l,tg)` Knd: `Knd` mk_lnk: `(link(n) from i to j)` id-graph-edge: `(i─→j)∈G` id-graph: `Graph(S)` Id: `Id` l_member: `(x ∈ l)` list: `T List` all: `∀x:A. B[x]` exists: `∃x:A. B[x]` iff: `P `⇐⇒` Q` and: `P ∧ Q` set: `{x:A| B[x]} ` apply: `f a` function: `x:A ─→ B[x]` equal: `s = 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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