Nuprl Lemma : hdf-state-single-val_wf
∀[A,B:Type]. ∀[X:hdataflow(A;B ⟶ B)]. ∀[b:B].
(hdf-state-single-val(X;b) ∈ hdataflow(A;B)) supposing (hdf-single-valued(X;A;B ⟶ B) and valueall-type(B))
Proof
Definitions occuring in Statement :
hdf-state-single-val: hdf-state-single-val(X;b),
hdf-single-valued: hdf-single-valued(X;A;B),
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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
hdf-state-single-val: hdf-state-single-val(X;b),
prop: ℙ,
hdf-ap: X(a),
subtype_rel: A ⊆r B,
ext-eq: A ≡ B,
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
ifthenelse: if b then t else f fi ,
btrue: tt,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
hdf-run: hdf-run(P),
hdf-single-valued: hdf-single-valued(X;A;B),
iterate-hdataflow: P*(inputs),
list_accum: list_accum,
nil: [],
it: ⋅,
bool: 𝔹,
unit: Unit,
uiff: uiff(P;Q),
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
pi1: fst(t),
top: Top,
nat: ℕ,
decidable: Dec(P),
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
hdf-halt: hdf-halt()
Latex:
\mforall{}[A,B:Type]. \mforall{}[X:hdataflow(A;B {}\mrightarrow{} B)]. \mforall{}[b:B].
(hdf-state-single-val(X;b) \mmember{} hdataflow(A;B)) supposing
(hdf-single-valued(X;A;B {}\mrightarrow{} B) and
valueall-type(B))
Date html generated:
2016_05_16-AM-10_40_31
Last ObjectModification:
2016_01_17-AM-11_13_28
Theory : halting!dataflow
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