Nuprl Lemma : pRun2_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])]. ∀[t:ℕ].
(pRun2(S0;env;nat2msg;loc2msg;t) ∈ {L:(ℤ × Id × Id × pMsg(P.M[P])? × System(P.M[P])) List| ||L|| = (t + 1) ∈ ℤ} )) \000Csupposing
(Continuous+(P.M[P]) and
(∀P:Type. value-type(M[P])) and
M[Top])
Proof
Definitions occuring in Statement :
pRun2: pRun2(S0;env;nat2msg;loc2msg;t),
pEnvType: pEnvType(T.M[T]),
System: System(P.M[P]),
pMsg: pMsg(P.M[P]),
Id: Id,
length: ||as||,
list: T List,
strong-type-continuous: Continuous+(T.F[T]),
nat: ℕ,
value-type: value-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
all: ∀x:A. B[x],
unit: Unit,
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
product: x:A × B[x],
union: left + right,
add: n + m,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
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,
top: Top,
and: P ∧ Q,
prop: ℙ,
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),
pRun2: pRun2(S0;env;nat2msg;loc2msg;t),
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,
so_lambda: λ2x.t[x],
so_apply: x[s],
id-fun: id-fun(T),
has-value: (a)↓,
System: System(P.M[P]),
spreadn: spread3,
select: L[n],
nil: [],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
cons: [a / b],
pRunInfo: pRunInfo(P.M[P]),
subtract: n - m
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])]. \mforall{}[t:\mBbbN{}].
(pRun2(S0;env;nat2msg;loc2msg;t) \mmember{} \{L:(\mBbbZ{} \mtimes{} Id \mtimes{} Id \mtimes{} pMsg(P.M[P])? \mtimes{} System(P.M[P])) List|
||L|| = (t + 1)\} )) supposing
(Continuous+(P.M[P]) and
(\mforall{}P:Type. value-type(M[P])) and
M[Top])
Date html generated:
2016_05_17-AM-10_41_18
Last ObjectModification:
2016_01_18-AM-00_21_42
Theory : process-model
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