Nuprl Lemma : hdf-parallel-bind-eq-gen
∀[A,B1,B2,C:Type]. ∀[X1:hdataflow(A;B1)]. ∀[X2:hdataflow(A;B2)]. ∀[Y1:B1 ⟶ hdataflow(A;C)]. ∀[Y2:B2 ⟶ hdataflow(A;C)].
(X1 >>= Y1 || X2 >>= Y2 = X1 + X2 >>= λb.case b of inl(b1) => Y1 b1 | inr(b2) => Y2 b2 ∈ hdataflow(A;C)) supposing
(valueall-type(C) and
valueall-type(B2) and
valueall-type(B1))
Proof
Definitions occuring in Statement :
hdf-bind: X >>= Y,
hdf-union: X + Y,
hdf-parallel: X || Y,
hdataflow: hdataflow(A;B),
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,
eclass-disju-program: xpr + ypr,
bind-class-program: xpr >>= ypr,
parallel-class-program: X || Y,
eclass1-program: eclass1-program(f;pr),
mkid: "$x",
Id: Id,
squash: ↓T,
prop: ℙ,
implies: P ⇒ Q,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[A,B1,B2,C:Type]. \mforall{}[X1:hdataflow(A;B1)]. \mforall{}[X2:hdataflow(A;B2)]. \mforall{}[Y1:B1 {}\mrightarrow{} hdataflow(A;C)].
\mforall{}[Y2:B2 {}\mrightarrow{} hdataflow(A;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(B2) and
valueall-type(B1))
Date html generated:
2016_05_17-AM-09_12_25
Last ObjectModification:
2016_01_17-PM-09_12_23
Theory : local!classes
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