Nuprl Lemma : system-strongly-realizes_functionality
∀[M:Type ⟶ Type]
∀n2m:ℕ ⟶ pMsg(P.M[P]). ∀l2m:Id ⟶ pMsg(P.M[P]).
∀[A:pEnvType(P.M[P]) ⟶ pRunType(P.M[P]) ⟶ ℙ]. ∀[B:EO+(pMsg(P.M[P])) ⟶ ℙ].
∀X,Y:InitialSystem(P.M[P]).
(system-equiv(P.M[P];X;Y) ⇒ assuming(env,r.A[env;r]) X |= eo.B[eo] ⇒ assuming(env,r.A[env;r]) Y |= eo.B[eo])
supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
system-strongly-realizes: system-strongly-realizes,
InitialSystem: InitialSystem(P.M[P]),
pEnvType: pEnvType(T.M[T]),
pRunType: pRunType(T.M[T]),
system-equiv: system-equiv(T.M[T];S1;S2),
pMsg: pMsg(P.M[P]),
event-ordering+: EO+(Info),
Id: Id,
strong-type-continuous: Continuous+(T.F[T]),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
strong-type-continuous: Continuous+(T.F[T]),
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
system-strongly-realizes: system-strongly-realizes,
system-realizes: system-realizes,
let: let,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
InitialSystem: InitialSystem(P.M[P]),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
System: System(P.M[P]),
sub-system: sub-system(P.M[P];S1;S2),
sublist: L1 ⊆ L2,
exists: ∃x:A. B[x],
int_seg: {i..j-},
decidable: Dec(P),
or: P ∨ Q,
std-initial: std-initial(S),
pi2: snd(t),
system-equiv: system-equiv(T.M[T];S1;S2),
pi1: fst(t),
ge: i ≥ j ,
guard: {T},
lelt: i ≤ j < k,
top: Top,
nat: ℕ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
less_than: a < b,
squash: ↓T,
cand: A c∧ B,
ldag: LabeledDAG(T),
le: A ≤ B,
sq_type: SQType(T),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
component: component(P.M[P]),
process-equiv: process-equiv,
less_than': less_than'(a;b),
inject: Inj(A;B;f)
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}n2m:\mBbbN{} {}\mrightarrow{} pMsg(P.M[P]). \mforall{}l2m:Id {}\mrightarrow{} pMsg(P.M[P]).
\mforall{}[A:pEnvType(P.M[P]) {}\mrightarrow{} pRunType(P.M[P]) {}\mrightarrow{} \mBbbP{}]. \mforall{}[B:EO+(pMsg(P.M[P])) {}\mrightarrow{} \mBbbP{}].
\mforall{}X,Y:InitialSystem(P.M[P]).
(system-equiv(P.M[P];X;Y)
{}\mRightarrow{} assuming(env,r.A[env;r])
X |= eo.B[eo]
{}\mRightarrow{} assuming(env,r.A[env;r])
Y |= eo.B[eo])
supposing Continuous+(P.M[P])
Date html generated:
2016_05_17-AM-11_05_20
Last ObjectModification:
2016_01_18-AM-00_27_32
Theory : process-model
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