Nuprl Lemma : hdf-compose1-ap
∀[A,B,C:Type]. ∀[X:hdataflow(A;B)]. ∀[f:B ⟶ C]. ∀[a:A].
f o X(a) ~ <f o (fst(X(a))), bag-map(f;snd(X(a)))> supposing valueall-type(C)
Proof
Definitions occuring in Statement :
hdf-compose1: f o X,
hdf-ap: X(a),
hdataflow: hdataflow(A;B),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
function: x:A ⟶ B[x],
pair: <a, b>,
universe: Type,
sqequal: s ~ t,
bag-map: bag-map(f;bs)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
hdf-ap: X(a),
hdf-compose1: f o X,
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
top: Top,
subtype_rel: A ⊆r B,
ext-eq: A ≡ B,
assert: ↑b,
bfalse: ff,
false: False,
prop: ℙ,
hdf-halt: hdf-halt(),
pi1: fst(t),
pi2: snd(t),
callbyvalueall: callbyvalueall,
evalall: evalall(t),
bag-map: bag-map(f;bs),
map: map(f;as),
list_ind: list_ind,
empty-bag: {},
nil: [],
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
has-value: (a)↓,
has-valueall: has-valueall(a),
not: ¬A,
true: True
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[X:hdataflow(A;B)]. \mforall{}[f:B {}\mrightarrow{} C]. \mforall{}[a:A].
f o X(a) \msim{} <f o (fst(X(a))), bag-map(f;snd(X(a)))> supposing valueall-type(C)
Date html generated:
2016_05_16-AM-10_39_24
Last ObjectModification:
2015_12_28-PM-07_44_53
Theory : halting!dataflow
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