Nuprl Lemma : hdf-memory_wf
∀[A,B:Type]. ∀[X:hdataflow(A;B ⟶ B)]. ∀[bs:bag(B)]. hdf-memory(X;bs) ∈ hdataflow(A;B) supposing valueall-type(B)
Proof
Definitions occuring in Statement :
hdf-memory: hdf-memory(X;bs),
hdataflow: hdataflow(A;B),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
hdf-memory: hdf-memory(X;bs),
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[A,B:Type]. \mforall{}[X:hdataflow(A;B {}\mrightarrow{} B)]. \mforall{}[bs:bag(B)].
hdf-memory(X;bs) \mmember{} hdataflow(A;B) supposing valueall-type(B)
Date html generated:
2016_05_16-AM-10_40_44
Last ObjectModification:
2015_12_28-PM-07_44_05
Theory : halting!dataflow
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