Nuprl Lemma : hdf-parallel-bind-halt-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)].
(∀inputs:A List
hdf-halted(X1 >>= Y1 || X2 >>= Y2*(inputs))
= hdf-halted(X1 + X2 >>= λx.case x of inl(b1) => Y1[b1] | inr(b2) => Y2[b2]*(inputs))) supposing
(valueall-type(C) and
valueall-type(B1) and
valueall-type(B2))
Proof
Definitions occuring in Statement :
hdf-bind: X >>= Y,
hdf-union: X + Y,
hdf-parallel: X || Y,
iterate-hdataflow: P*(inputs),
hdf-halted: hdf-halted(P),
hdataflow: hdataflow(A;B),
list: T List,
valueall-type: valueall-type(T),
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
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,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s],
sq_type: SQType(T),
guard: {T},
compose: f o g,
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
prop: ℙ,
subtype_rel: A ⊆r B
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)].
(\mforall{}inputs:A List
hdf-halted(X1 >>= Y1 || X2 >>= Y2*(inputs))
= hdf-halted(X1 + X2
>>= \mlambda{}x.case x of inl(b1) => Y1[b1] | inr(b2) => Y2[b2]*(inputs))) supposing
(valueall-type(C) and
valueall-type(B1) and
valueall-type(B2))
Date html generated:
2016_05_17-AM-09_12_08
Last ObjectModification:
2016_01_17-PM-09_12_47
Theory : local!classes
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