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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