Nuprl Lemma : pi-run-example_wf
∀[P:pi_term()]. ∀[t:ℕ].
(pi-run-example{$a,$b,$c,$d,$e,$f,$g,$h,$i,$j,$k}(P;t) ∈ {L:(ℤ × Id × Id × pMsg(P.piM(P))? × System(P.piM(P))) List|
||L|| = (t + 1) ∈ ℤ} )
Proof
Definitions occuring in Statement :
pi-run-example: pi-run-example{$l_server,$l_choose,$l_comm,$l_pi,$a,$b,$c,$d,$e,$f,$g}(P;t),
piM: piM(T),
pi_term: pi_term(),
System: System(P.M[P]),
pMsg: pMsg(P.M[P]),
Id: Id,
length: ||as||,
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
set: {x:A| B[x]} ,
product: x:A × B[x],
union: left + right,
add: n + m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
pi-run-example: pi-run-example{$l_server,$l_choose,$l_comm,$l_pi,$a,$b,$c,$d,$e,$f,$g}(P;t),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
piM: piM(T),
all: ∀x:A. B[x],
PiDataVal: PiDataVal(),
subtype_rel: A ⊆r B,
pMsg: pMsg(P.M[P]),
mkid: "$x",
Id: Id
Latex:
\mforall{}[P:pi\_term()]. \mforall{}[t:\mBbbN{}].
(pi-run-example\{\$a,\$b,\$c,\$d,\$e,\$f,\$g,\$h,\$i,\$j,\$k\}(P;t)
\mmember{} \{L:(\mBbbZ{} \mtimes{} Id \mtimes{} Id \mtimes{} pMsg(P.piM(P))? \mtimes{} System(P.piM(P))) List| ||L|| = (t + 1)\} )
Date html generated:
2016_05_17-AM-11_35_43
Last ObjectModification:
2015_12_29-PM-06_48_05
Theory : event-logic-applications
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