Nuprl Lemma : do-chosen-command_wf
∀[M:Type ⟶ Type]
∀[nat2msg:ℕ ⟶ pMsg(P.M[P])]. ∀[loc2msg:Id ⟶ pMsg(P.M[P])]. ∀[S:System(P.M[P])]. ∀[t,n,m:ℕ]. ∀[nm:Id].
(do-chosen-command(nat2msg;loc2msg;t;S;n;m;nm) ∈ ℤ × Id × Id × pMsg(P.M[P])? × System(P.M[P]))
supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
do-chosen-command: do-chosen-command(nat2msg;loc2msg;t;S;n;m;nm),
System: System(P.M[P]),
pMsg: pMsg(P.M[P]),
Id: Id,
strong-type-continuous: Continuous+(T.F[T]),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
union: left + right,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
do-chosen-command: do-chosen-command(nat2msg;loc2msg;t;S;n;m;nm),
let: let,
System: System(P.M[P]),
so_lambda: λ2x.t[x],
so_apply: x[s],
ldag: LabeledDAG(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
lg-is-source: lg-is-source(g;i),
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
subtype_rel: A ⊆r B,
prop: ℙ,
pInTransit: pInTransit(P.M[P]),
spreadn: spread3,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}[nat2msg:\mBbbN{} {}\mrightarrow{} pMsg(P.M[P])]. \mforall{}[loc2msg:Id {}\mrightarrow{} pMsg(P.M[P])]. \mforall{}[S:System(P.M[P])]. \mforall{}[t,n,m:\mBbbN{}].
\mforall{}[nm:Id].
(do-chosen-command(nat2msg;loc2msg;t;S;n;m;nm) \mmember{} \mBbbZ{} \mtimes{} Id \mtimes{} Id \mtimes{} pMsg(P.M[P])? \mtimes{} System(P.M[P]))
supposing Continuous+(P.M[P])
Date html generated:
2016_05_17-AM-10_39_24
Last ObjectModification:
2015_12_29-PM-05_25_32
Theory : process-model
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