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 i j) from i to j),b) ∈ Knd)))
Proof
Definitions occuring in Statement :
graph-rcvset: graph-rcvset(a;b;S;G;k),
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,
assert: ↑b,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
equal: s = 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.
(\muparrow{}graph-rcvset(a;b;S;G;k)
\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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