### 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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