Nuprl Lemma : hdf-comb3_wf

∀[A,C,B1,B2,B3:Type]. ∀[f:B1 ⟶ B2 ⟶ B3 ⟶ bag(C)]. ∀[X:hdataflow(A;B1)]. ∀[Y:hdataflow(A;B2)]. ∀[Z:hdataflow(A;B3)].
  hdf-comb3(f;X;Y;Z) ∈ hdataflow(A;C) supposing ((↓B2) ∧ (↓B3)) ∧ valueall-type(C)


Proof




Definitions occuring in Statement :  hdf-comb3: hdf-comb3(f;X;Y;Z),  hdataflow: hdataflow(A;B),  valueall-type: valueall-type(T),  uimplies: b supposing a,  uall: ∀[x:A]. B[x],  squash: ↓T,  and: P ∧ Q,  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: b supposing a,  hdf-comb3: hdf-comb3(f;X;Y;Z),  and: P ∧ Q,  so_lambda: λ2x.t[x],  so_apply: x[s],  squash: ↓T,  exists: ∃x:A. B[x],  prop: ℙ

Latex:
\mforall{}[A,C,B1,B2,B3:Type].  \mforall{}[f:B1  {}\mrightarrow{}  B2  {}\mrightarrow{}  B3  {}\mrightarrow{}  bag(C)].  \mforall{}[X:hdataflow(A;B1)].  \mforall{}[Y:hdataflow(A;B2)].
\mforall{}[Z:hdataflow(A;B3)].
    hdf-comb3(f;X;Y;Z)  \mmember{}  hdataflow(A;C)  supposing  ((\mdownarrow{}B2)  \mwedge{}  (\mdownarrow{}B3))  \mwedge{}  valueall-type(C)



Date html generated: 2016_05_16-AM-10_40_52
Last ObjectModification: 2016_01_17-AM-11_12_16

Theory : halting!dataflow


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