Nuprl Lemma : mk-hdf_wf
∀[A,B,S:Type]. ∀[s0:S]. ∀[H:S ⟶ 𝔹]. ∀[G:S ⟶ A ⟶ (S × bag(B))]. (mk-hdf(s,m.G[s;m];s.H[s];s0) ∈ hdataflow(A;B))
Proof
Definitions occuring in Statement :
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
hdataflow: hdataflow(A;B),
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
hdataflow: hdataflow(A;B),
corec: corec(T.F[T]),
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
so_apply: x[s],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
hdf-halt: hdf-halt(),
nequal: a ≠ b ∈ T ,
hdf-run: hdf-run(P),
so_apply: x[s1;s2]
Latex:
\mforall{}[A,B,S:Type]. \mforall{}[s0:S]. \mforall{}[H:S {}\mrightarrow{} \mBbbB{}]. \mforall{}[G:S {}\mrightarrow{} A {}\mrightarrow{} (S \mtimes{} bag(B))].
(mk-hdf(s,m.G[s;m];s.H[s];s0) \mmember{} hdataflow(A;B))
Date html generated:
2016_05_16-AM-10_38_55
Last ObjectModification:
2016_01_17-AM-11_12_50
Theory : halting!dataflow
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