Nuprl Lemma : iterate-hdf-bind-simple
∀[A,B,C:Type]. ∀[X:hdataflow(A;B)]. ∀[Y:B ⟶ hdataflow(A;C)].
∀[L:A List]. ∀[a:A]. ((snd(X >>= Y*(L)(a))) = (snd(simple-hdf-bind(X;Y)*(L)(a))) ∈ bag(C)) supposing valueall-type(C)
Proof
Definitions occuring in Statement :
simple-hdf-bind: simple-hdf-bind(X;Y),
hdf-bind: X >>= Y,
iterate-hdataflow: P*(inputs),
hdf-ap: X(a),
hdataflow: hdataflow(A;B),
list: T List,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi2: snd(t),
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
simple-hdf-bind: simple-hdf-bind(X;Y),
hdf-bind: X >>= Y,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
bfalse: ff,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
squash: ↓T,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
not: ¬A,
false: False,
ext-eq: A ≡ B,
hdf-run: hdf-run(P),
hdf-ap: X(a),
hdf-halt: hdf-halt(),
hdf-halted: hdf-halted(P),
isr: isr(x),
assert: ↑b,
pi2: snd(t),
simple-bind-nxt: simple-bind-nxt(Y; p; a),
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
pi1: fst(t),
true: True,
bind-nxt: bind-nxt(Y;p;a),
cand: A c∧ B,
decidable: Dec(P),
or: P ∨ Q,
sq_type: SQType(T),
compose: f o g,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[X:hdataflow(A;B)]. \mforall{}[Y:B {}\mrightarrow{} hdataflow(A;C)].
\mforall{}[L:A List]. \mforall{}[a:A]. ((snd(X >>= Y*(L)(a))) = (snd(simple-hdf-bind(X;Y)*(L)(a))))
supposing valueall-type(C)
Date html generated:
2016_05_16-AM-10_44_15
Last ObjectModification:
2016_01_17-AM-11_13_54
Theory : halting!dataflow
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