Nuprl Lemma : hdf-parallel-bind-halt-eq
∀[A,B,C:Type]. ∀[X1,X2:hdataflow(A;B)]. ∀[X:B ⟶ hdataflow(A;C)].
(∀inputs:A List. hdf-halted(X1 >>= X || X2 >>= X*(inputs)) = hdf-halted(X1 || X2 >>= X*(inputs))) supposing
(valueall-type(C) and
valueall-type(B))
Proof
Definitions occuring in Statement :
hdf-bind: 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],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
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],
hdf-bind: X >>= Y,
implies: P ⇒ Q,
hdf-bind-gen: X (hdfs) >>= Y,
exists: ∃x:A. B[x],
prop: ℙ,
and: P ∧ Q,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
hdf-parallel: X || Y,
bind-nxt: bind-nxt(Y;p;a),
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
band: p ∧b q,
ifthenelse: if b then t else f fi ,
hdf-ap: X(a),
hdf-halt: hdf-halt(),
exposed-bfalse: exposed-bfalse,
callbyvalueall: callbyvalueall,
evalall: evalall(t),
empty-bag: {},
nil: [],
bfalse: ff,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
iff: P ⇐⇒ Q,
cand: A c∧ B,
rev_implies: P ⇐ Q,
true: True,
pi1: fst(t),
subtype_rel: A ⊆r B,
has-value: (a)↓,
has-valueall: has-valueall(a),
pi2: snd(t),
squash: ↓T
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[X1,X2:hdataflow(A;B)]. \mforall{}[X:B {}\mrightarrow{} hdataflow(A;C)].
(\mforall{}inputs:A List
hdf-halted(X1 >>= X || X2 >>= X*(inputs)) = hdf-halted(X1 || X2 >>= X*(inputs))) supposing
(valueall-type(C) and
valueall-type(B))
Date html generated:
2016_05_17-AM-09_12_05
Last ObjectModification:
2016_01_17-PM-09_18_07
Theory : local!classes
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