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]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
exists: ∃x:A. B[x],
Knd: Knd,
IdLnk: IdLnk,
Id: Id,
sq_type: SQType(T),
guard: {T},
hasloc: hasloc(k;i),
top: Top,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
btrue: tt,
not: ¬A,
false: False,
uiff: uiff(P;Q),
rev_implies: P ⇐ Q
Latex:
\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:
2016_05_16-AM-11_00_15
Last ObjectModification:
2015_12_29-AM-09_11_20
Theory : event-ordering
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