Nuprl Lemma : bind-nxt_wf
∀[A,B,C:Type]. ∀[Y:B ⟶ hdataflow(A;C)]. ∀[p:hdataflow(A;B) × bag(hdataflow(A;C))]. ∀[a:A].
bind-nxt(Y;p;a) ∈ hdataflow(A;B) × bag(hdataflow(A;C)) × bag(C) supposing valueall-type(C)
Proof
Definitions occuring in Statement :
bind-nxt: bind-nxt(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,
bind-nxt: bind-nxt(Y;p;a),
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
prop: ℙ,
pi1: fst(t),
pi2: snd(t),
subtype_rel: A ⊆r B
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[Y:B {}\mrightarrow{} hdataflow(A;C)]. \mforall{}[p:hdataflow(A;B) \mtimes{} bag(hdataflow(A;C))]. \mforall{}[a:A].
bind-nxt(Y;p;a) \mmember{} hdataflow(A;B) \mtimes{} bag(hdataflow(A;C)) \mtimes{} bag(C) supposing valueall-type(C)
Date html generated:
2016_05_16-AM-10_42_39
Last ObjectModification:
2016_01_17-AM-11_11_42
Theory : halting!dataflow
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