Nuprl Lemma : parallel-compose2-program-eq
∀[Info,B,C:Type]. ∀[X1,X2:Id ⟶ hdataflow(Info;B ⟶ bag(C))]. ∀[X:Id ⟶ hdataflow(Info;B)].
(X1 o X || X2 o X = X1 || X2 o X ∈ (Id ⟶ hdataflow(Info;C))) supposing
(valueall-type(C) and
valueall-type(B) and
(↓B))
Proof
Definitions occuring in Statement :
parallel-class-program: X || Y,
eclass2-program: Xpr o Ypr,
hdataflow: hdataflow(A;B),
Id: Id,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
squash: ↓T,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
squash: ↓T,
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
class-ap: X(e),
hdataflow-class: hdataflow-class(F),
pi2: snd(t),
hdf-ap: X(a),
iterate-hdataflow: P*(inputs),
list_accum: list_accum,
map: map(f;as),
list_ind: list_ind,
es-before: before(e),
ifthenelse: if b then t else f fi ,
es-first: first(e),
bor: p ∨bq,
es-eq-E: e = e',
es-eq: es-eq(es),
band: p ∧b q,
eq_id: a = b,
id-deq: IdDeq,
atom2-deq: Atom2Deq,
eq_atom: eq_atom$n(x;y),
es-loc: loc(e),
record-select: r.x,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
local-class: LocalClass(X),
sq_exists: ∃x:{A| B[x]},
implies: P ⇒ Q,
prop: ℙ,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
true: True,
parallel-class-program: X || Y,
eclass2-program: Xpr o Ypr,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
bfalse: ff,
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X1,X2:Id {}\mrightarrow{} hdataflow(Info;B {}\mrightarrow{} bag(C))]. \mforall{}[X:Id {}\mrightarrow{} hdataflow(Info;B)].
(X1 o X || X2 o X = X1 || X2 o X) supposing (valueall-type(C) and valueall-type(B) and (\mdownarrow{}B))
Date html generated:
2016_05_17-AM-09_08_46
Last ObjectModification:
2016_01_17-PM-09_14_28
Theory : local!classes
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