Nuprl Lemma : graph-rcvs_wf2
∀[S:Id List]. ∀[G:Graph(S)]. ∀[a:Id ─→ Id ─→ Id]. ∀[b:Id]. ∀[j:{j:Id| (j ∈ S)} ].
(graph-rcvs(S;G;a;b;j) ∈ {k:Knd| ↑hasloc(k;j)} List)
Proof
Definitions occuring in Statement :
hasloc: hasloc(k;i),
graph-rcvs: graph-rcvs(S;G;a;b;j),
Knd: Knd,
id-graph: Graph(S),
Id: Id,
l_member: (x ∈ l),
list: T List,
assert: ↑b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ─→ B[x]
Lemmas :
list-subtype,
list_wf,
l_member_wf,
set_wf,
Id_wf,
id-graph_wf,
assert_wf,
hasloc_wf,
subtype_rel_list_set,
member-graph-rcvs,
subtype_base_sq,
Knd_wf,
union_subtype_base,
IdLnk_wf,
product_subtype_base,
atom2_subtype_base,
isrcv_rcv_lemma,
lnk_rcv_lemma,
ldst_mk_lnk_lemma,
bnot_wf,
eq_id_wf,
not_wf,
equal_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
assert-eq-id
\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)\} ].
(graph-rcvs(S;G;a;b;j) \mmember{} \{k:Knd| \muparrow{}hasloc(k;j)\} List)
Date html generated:
2015_07_17-AM-09_14_02
Last ObjectModification:
2015_01_28-AM-07_56_09
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