Nuprl Lemma : parallel-bind-program-eq
∀[Info,B,C:Type]. ∀[X1,X2:Id ⟶ hdataflow(Info;B)]. ∀[X:B ⟶ Id ⟶ hdataflow(Info;C)].
(X1 >>= X || X2 >>= X = X1 || X2 >>= X ∈ (Id ⟶ hdataflow(Info;C))) supposing (valueall-type(C) and valueall-type(B))
Proof
Definitions occuring in Statement :
parallel-class-program: X || Y,
bind-class-program: xpr >>= ypr,
hdataflow: hdataflow(A;B),
Id: Id,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
local-class: LocalClass(X),
implies: P ⇒ Q,
prop: ℙ,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
parallel-class-program: X || Y,
bind-class-program: xpr >>= ypr,
class-ap: X(e),
hdataflow-class: hdataflow-class(F),
pi2: snd(t),
hdf-ap: X(a),
iterate-hdataflow: P*(inputs),
list_accum: list_accum,
map: map(f;as),
list_ind: list_ind,
es-before: before(e),
ifthenelse: if b then t else f fi ,
es-first: first(e),
bor: p ∨bq,
es-eq-E: e = e',
es-eq: es-eq(es),
band: p ∧b q,
eq_id: a = b,
id-deq: IdDeq,
atom2-deq: Atom2Deq,
eq_atom: eq_atom$n(x;y),
es-loc: loc(e),
record-select: r.x,
sq_exists: ∃x:{A| B[x]}
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X1,X2:Id {}\mrightarrow{} hdataflow(Info;B)]. \mforall{}[X:B {}\mrightarrow{} Id {}\mrightarrow{} hdataflow(Info;C)].
(X1 >>= X || X2 >>= X = X1 || X2 >>= X) supposing (valueall-type(C) and valueall-type(B))
Date html generated:
2016_05_17-AM-09_12_11
Last ObjectModification:
2016_01_17-PM-09_14_36
Theory : local!classes
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