Nuprl Lemma : rec-bind-nxt_wf
∀[A,B,C:Type]. ∀[X:C ⟶ hdataflow(A;B)]. ∀[Y:C ⟶ hdataflow(A;C)]. ∀[p:bag(hdataflow(A;B)) × bag(hdataflow(A;C))].
∀[a:A].
(rec-bind-nxt(X;Y;p;a) ∈ bag(hdataflow(A;B)) × bag(hdataflow(A;C)) × bag(B)) supposing
(valueall-type(B) and
valueall-type(C))
Proof
Definitions occuring in Statement :
rec-bind-nxt: rec-bind-nxt(X;Y;p;a),
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],
product: 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,
rec-bind-nxt: rec-bind-nxt(X;Y;p;a),
let: let,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
callbyvalueall: callbyvalueall,
squash: ↓T,
has-value: (a)↓,
has-valueall: has-valueall(a),
pi2: snd(t),
hdf-running: hdf-running(P),
pi1: fst(t),
prop: ℙ,
subtype_rel: A ⊆r B
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[X:C {}\mrightarrow{} hdataflow(A;B)]. \mforall{}[Y:C {}\mrightarrow{} hdataflow(A;C)].
\mforall{}[p:bag(hdataflow(A;B)) \mtimes{} bag(hdataflow(A;C))]. \mforall{}[a:A].
(rec-bind-nxt(X;Y;p;a) \mmember{} bag(hdataflow(A;B)) \mtimes{} bag(hdataflow(A;C)) \mtimes{} bag(B)) supposing
(valueall-type(B) and
valueall-type(C))
Date html generated:
2016_05_16-AM-10_44_33
Last ObjectModification:
2016_01_17-AM-11_12_28
Theory : halting!dataflow
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