Nuprl Lemma : hdf-comb2_wf
∀[A,B,C,D:Type]. ∀[X:hdataflow(A;B)]. ∀[Y:hdataflow(A;C)]. ∀[f:B ⟶ C ⟶ bag(D)].
hdf-comb2(f;X;Y) ∈ hdataflow(A;D) supposing (↓C) ∧ valueall-type(D)
Proof
Definitions occuring in Statement :
hdf-comb2: hdf-comb2(f;X;Y),
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-comb2: hdf-comb2(f;X;Y),
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T,
exists: ∃x:A. B[x],
prop: ℙ
Latex:
\mforall{}[A,B,C,D:Type]. \mforall{}[X:hdataflow(A;B)]. \mforall{}[Y:hdataflow(A;C)]. \mforall{}[f:B {}\mrightarrow{} C {}\mrightarrow{} bag(D)].
hdf-comb2(f;X;Y) \mmember{} hdataflow(A;D) supposing (\mdownarrow{}C) \mwedge{} valueall-type(D)
Date html generated:
2016_05_16-AM-10_40_48
Last ObjectModification:
2016_01_17-AM-11_12_13
Theory : halting!dataflow
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