Nuprl Lemma : parallel-bind-program-eq-gen
∀[Info,B1,B2,C:Type]. ∀[X1:Id ⟶ hdataflow(Info;B1)]. ∀[X2:Id ⟶ hdataflow(Info;B2)].
∀[Y1:B1 ⟶ Id ⟶ hdataflow(Info;C)]. ∀[Y2:B2 ⟶ Id ⟶ hdataflow(Info;C)].
(X1 >>= Y1 || X2 >>= Y2
= X1 + X2 >>= λb.case b of inl(b1) => Y1 b1 | inr(b2) => Y2 b2
∈ (Id ⟶ hdataflow(Info;C))) supposing
(valueall-type(C) and
valueall-type(B1) and
valueall-type(B2))
Proof
Definitions occuring in Statement :
eclass-disju-program: xpr + ypr,
parallel-class-program: X || Y,
bind-class-program: xpr >>= ypr,
hdataflow: hdataflow(A;B),
Id: Id,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
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,
subtype_rel: A ⊆r B,
local-class: LocalClass(X),
sq_exists: ∃x:{A| B[x]},
implies: P ⇒ Q,
prop: ℙ,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
eclass-disju-program: xpr + ypr,
bind-class-program: xpr >>= ypr,
parallel-class-program: X || Y,
eclass1-program: eclass1-program(f;pr),
top: Top
Latex:
\mforall{}[Info,B1,B2,C:Type]. \mforall{}[X1:Id {}\mrightarrow{} hdataflow(Info;B1)]. \mforall{}[X2:Id {}\mrightarrow{} hdataflow(Info;B2)].
\mforall{}[Y1:B1 {}\mrightarrow{} Id {}\mrightarrow{} hdataflow(Info;C)]. \mforall{}[Y2:B2 {}\mrightarrow{} Id {}\mrightarrow{} hdataflow(Info;C)].
(X1 >>= Y1 || X2 >>= Y2 = X1 + X2 >>= \mlambda{}b.case b of inl(b1) => Y1 b1 | inr(b2) => Y2 b2) supposing
(valueall-type(C) and
valueall-type(B1) and
valueall-type(B2))
Date html generated:
2016_05_17-AM-09_12_16
Last ObjectModification:
2016_01_17-PM-09_15_44
Theory : local!classes
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