Nuprl Lemma : hdf-rec-bind_wf
∀[A,B,C:Type]. ∀[X:C ⟶ hdataflow(A;B)]. ∀[Y:C ⟶ hdataflow(A;C)].
(hdf-rec-bind(X;Y) ∈ C ⟶ hdataflow(A;B)) supposing (valueall-type(B) and valueall-type(C))
Proof
Definitions occuring in Statement :
hdf-rec-bind: hdf-rec-bind(X;Y),
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-rec-bind: hdf-rec-bind(X;Y),
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
bfalse: ff,
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[X:C {}\mrightarrow{} hdataflow(A;B)]. \mforall{}[Y:C {}\mrightarrow{} hdataflow(A;C)].
(hdf-rec-bind(X;Y) \mmember{} C {}\mrightarrow{} hdataflow(A;B)) supposing (valueall-type(B) and valueall-type(C))
Date html generated:
2016_05_16-AM-10_44_40
Last ObjectModification:
2015_12_28-PM-07_41_20
Theory : halting!dataflow
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