Nuprl Lemma : iterate-hdf-buffer2-simple
∀[A,B:Type]. ∀[X:hdataflow(A;B ⟶ B)]. ∀[bs:bag(B)].
∀[L:A List]. ∀[a:A]. ((snd(hdf-buffer2(X;bs)*(L)(a))) = (snd(simple-hdf-buffer2(X;bs)*(L)(a))) ∈ bag(B))
supposing valueall-type(B)
Proof
Definitions occuring in Statement :
hdf-buffer2: hdf-buffer2(X;bs),
simple-hdf-buffer2: simple-hdf-buffer2(X;bs),
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-buffer2: simple-hdf-buffer2(X;bs),
hdf-buffer2: hdf-buffer2(X;bs),
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
or: P ∨ Q,
ext-eq: A ≡ B,
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
hdf-ap: X(a),
hdf-run: hdf-run(P),
hdf-halt: hdf-halt(),
hdf-halted: hdf-halted(P),
ifthenelse: if b then t else f fi ,
isr: isr(x),
bfalse: ff,
btrue: tt,
callbyvalueall: callbyvalueall,
evalall: evalall(t),
bag-combine: ⋃x∈bs.f[x],
bag-union: bag-union(bbs),
concat: concat(ll),
reduce: reduce(f;k;as),
list_ind: list_ind,
bag-map: bag-map(f;bs),
map: map(f;as),
empty-bag: {},
nil: [],
it: ⋅,
bag-null: bag-null(bs),
null: null(as),
pi2: snd(t),
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T},
decidable: Dec(P),
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
pi1: fst(t),
has-value: (a)↓,
has-valueall: has-valueall(a),
iterate-hdataflow: P*(inputs),
list_accum: list_accum
Latex:
\mforall{}[A,B:Type]. \mforall{}[X:hdataflow(A;B {}\mrightarrow{} B)]. \mforall{}[bs:bag(B)].
\mforall{}[L:A List]. \mforall{}[a:A]. ((snd(hdf-buffer2(X;bs)*(L)(a))) = (snd(simple-hdf-buffer2(X;bs)*(L)(a))))
supposing valueall-type(B)
Date html generated:
2016_05_16-AM-10_44_25
Last ObjectModification:
2016_01_17-AM-11_13_12
Theory : halting!dataflow
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