Nuprl Lemma : pi-system_wf
∀[f:(Id List) ⟶ Id]. ∀[l_server,l_choose,l_comm,l_pi:Id].
(pi-system(f;l_server;l_choose;l_comm;l_pi) ∈ pi_term() ⟶ System(P.piM(P)))
Proof
Definitions occuring in Statement :
pi-system: pi-system(f;l_server;l_choose;l_comm;l_pi),
piM: piM(T),
pi_term: pi_term(),
System: System(P.M[P]),
Id: Id,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
pi-system: pi-system(f;l_server;l_choose;l_comm;l_pi),
System: System(P.M[P]),
so_lambda: λ2x.t[x],
so_apply: x[s],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
pInTransit: pInTransit(P.M[P]),
pCom: pCom(P.M[P]),
Com: Com(P.M[P]),
mk-tagged: mk-tagged(tg;x),
tagged+: T |+ z:B,
isect2: T1 ⋂ T2,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
rev_uimplies: rev_uimplies(P;Q),
eq_atom: x =a y,
assert: ↑b,
true: True,
piM: piM(T),
bfalse: ff,
bnot: ¬bb,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
top: Top
Latex:
\mforall{}[f:(Id List) {}\mrightarrow{} Id]. \mforall{}[l$_{server}$,l$_{choose}$,l$\mbackslash{}ff5\000Cf{comm}$,l$_{pi}$:Id].
(pi-system(f;l$_{server}$;l$_{choose}$;l$_{com\000Cm}$;l$_{pi}$) \mmember{} pi\_term() {}\mrightarrow{} System(P.piM(P)))
Date html generated:
2016_05_17-AM-11_35_23
Last ObjectModification:
2015_12_29-PM-06_49_59
Theory : event-logic-applications
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