Nuprl Lemma : pRun_wf
∀[M:Type ⟶ Type]
∀[nat2msg:ℕ ⟶ pMsg(P.M[P])]. ∀[loc2msg:Id ⟶ pMsg(P.M[P])]. ∀[S0:System(P.M[P])]. ∀[env:pEnvType(P.M[P])].
(pRun(S0;env;nat2msg;loc2msg) ∈ fulpRunType(P.M[P]))
supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
pRun: pRun(S0;env;nat2msg;loc2msg),
pEnvType: pEnvType(T.M[T]),
fulpRunType: fulpRunType(T.M[T]),
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],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
fulpRunType: fulpRunType(T.M[T]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
and: P ∧ Q,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
pRun: pRun(S0;env;nat2msg;loc2msg),
ycomb: Y,
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
int_upper: {i...},
less_than: a < b,
System: System(P.M[P]),
spreadn: spread3
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}[nat2msg:\mBbbN{} {}\mrightarrow{} pMsg(P.M[P])]. \mforall{}[loc2msg:Id {}\mrightarrow{} pMsg(P.M[P])]. \mforall{}[S0:System(P.M[P])].
\mforall{}[env:pEnvType(P.M[P])].
(pRun(S0;env;nat2msg;loc2msg) \mmember{} fulpRunType(P.M[P]))
supposing Continuous+(P.M[P])
Date html generated:
2016_05_17-AM-10_40_25
Last ObjectModification:
2016_01_18-AM-00_15_17
Theory : process-model
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