Nuprl Lemma : assert-graph-rcvset

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


Definitions occuring in Statement :  graph-rcvset: graph-rcvset(a;b;S;G;k) 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 assert: b all: x:A. B[x] exists: x:A. B[x] iff: ⇐⇒ Q and: P ∧ Q apply: a function: x:A ─→ B[x] equal: t ∈ T
Lemmas :  assert_wf graph-rcvset_wf exists_wf Id_wf l_member_wf id-graph-edge_wf Knd_wf rcv_wf mk_lnk_wf id-graph_wf list_wf deq-member_wf id-deq_wf bool_wf eqtt_to_assert assert-deq-member eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot eq_id_wf assert-eq-id subtype_rel_list bfalse_wf false_wf iff_transitivity iff_weakening_uiff assert_of_band and_wf atom2_subtype_base id-graph-edge-implies-member union_subtype_base IdLnk_wf product_subtype_base isrcv_rcv_lemma tag_rcv_lemma lnk_rcv_lemma lname_mk_lnk_lemma lsrc_mk_lnk_lemma ldst_mk_lnk_lemma member_wf
\mforall{}a:Id  {}\mrightarrow{}  Id  {}\mrightarrow{}  Id.  \mforall{}b:Id.  \mforall{}S:Id  List.  \mforall{}G:Graph(S).  \mforall{}k:Knd.
    \mLeftarrow{}{}\mRightarrow{}  \mexists{}i,j:Id.  ((i  \mmember{}  S)  \mwedge{}  (j  \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_29
Last ObjectModification: 2015_01_28-AM-07_59_49

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