Nuprl Lemma : hdf-compose0-bag_wf

[A,B,C:Type]. ∀[f:bag(B) ⟶ bag(C)]. ∀[X:hdataflow(A;B)].
  hdf-compose0-bag(f;X) ∈ hdataflow(A;C) supposing valueall-type(C)


Proof




Definitions occuring in Statement :  hdf-compose0-bag: hdf-compose0-bag(f;X) hdataflow: hdataflow(A;B) valueall-type: valueall-type(T) uimplies: supposing a uall: [x:A]. B[x] member: t ∈ T function: x:A ⟶ B[x] universe: Type bag: bag(T)
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a hdf-compose0-bag: hdf-compose0-bag(f;X) so_lambda: λ2x.t[x] so_apply: x[s] so_lambda: λ2y.t[x; y] all: x:A. B[x] implies:  Q callbyvalueall: callbyvalueall has-value: (a)↓ has-valueall: has-valueall(a) so_apply: x[s1;s2]

Latex:
\mforall{}[A,B,C:Type].  \mforall{}[f:bag(B)  {}\mrightarrow{}  bag(C)].  \mforall{}[X:hdataflow(A;B)].
    hdf-compose0-bag(f;X)  \mmember{}  hdataflow(A;C)  supposing  valueall-type(C)



Date html generated: 2016_05_16-AM-10_39_42
Last ObjectModification: 2015_12_28-PM-07_44_03

Theory : halting!dataflow


Home Index