Nuprl Lemma : hdf-halted-compose2-iterate
∀[A,B,C:Type]. ∀[inputs:A List]. ∀[X1:hdataflow(A;B ⟶ bag(C))]. ∀[X2:hdataflow(A;B)].
hdf-halted(X1 o X2*(inputs)) = hdf-halted(X1*(inputs)) ∨bhdf-halted(X2*(inputs)) supposing valueall-type(C)
Proof
Definitions occuring in Statement :
hdf-compose2: X o Y,
iterate-hdataflow: P*(inputs),
hdf-halted: hdf-halted(P),
hdataflow: hdataflow(A;B),
list: T List,
bor: p ∨bq,
valueall-type: valueall-type(T),
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
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,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
top: Top,
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
true: True,
pi1: fst(t),
subtype_rel: A ⊆r B,
guard: {T},
squash: ↓T
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[inputs:A List]. \mforall{}[X1:hdataflow(A;B {}\mrightarrow{} bag(C))]. \mforall{}[X2:hdataflow(A;B)].
hdf-halted(X1 o X2*(inputs)) = hdf-halted(X1*(inputs)) \mvee{}\msubb{}hdf-halted(X2*(inputs))
supposing valueall-type(C)
Date html generated:
2016_05_16-AM-10_39_49
Last ObjectModification:
2016_01_17-AM-11_12_48
Theory : halting!dataflow
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