Nuprl Lemma : hdf-cbva-simple_wf
∀[U,T:Type]. ∀[m:ℕ+]. ∀[A:ℕm ⟶ ValueAllType]. ∀[L:U ⟶ i:ℕm ⟶ funtype(i;λk.bag(A k);bag(A i))].
(hdf-cbva-simple(L;m) ∈ hdataflow(U;A (m - 1)))
Proof
Definitions occuring in Statement :
hdf-cbva-simple: hdf-cbva-simple(L;m),
hdataflow: hdataflow(A;B),
int_seg: {i..j-},
nat_plus: ℕ+,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
subtract: n - m,
natural_number: $n,
universe: Type,
bag: bag(T),
funtype: funtype(n;A;T)
Definitions unfolded in proof :
vatype: ValueAllType,
hdataflow: hdataflow(A;B),
corec: corec(T.F[T]),
member: t ∈ T,
uall: ∀[x:A]. B[x],
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,
hdf-cbva-simple: hdf-cbva-simple(L;m),
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,
nequal: a ≠ b ∈ T ,
nat_plus: ℕ+,
int_seg: {i..j-},
lelt: i ≤ j < k,
subtype_rel: A ⊆r B,
sq_stable: SqStable(P),
squash: ↓T,
so_apply: x[s],
le: A ≤ B,
less_than': less_than'(a;b)
Latex:
\mforall{}[U,T:Type]. \mforall{}[m:\mBbbN{}\msupplus{}]. \mforall{}[A:\mBbbN{}m {}\mrightarrow{} ValueAllType]. \mforall{}[L:U {}\mrightarrow{} i:\mBbbN{}m {}\mrightarrow{} funtype(i;\mlambda{}k.bag(A k);bag(A i))].
(hdf-cbva-simple(L;m) \mmember{} hdataflow(U;A (m - 1)))
Date html generated:
2016_05_16-AM-10_44_47
Last ObjectModification:
2016_01_17-AM-11_12_25
Theory : halting!dataflow
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