Nuprl Lemma : parallel-class-program-eq
∀[Info,B:Type].
∀[X,Y:EClass(B)]. ∀[Xpr1,Xpr2:LocalClass(X)]. ∀[Ypr1,Ypr2:LocalClass(Y)].
(Xpr1 || Ypr1 = Xpr2 || Ypr2 ∈ (Id ⟶ hdataflow(Info;B))) supposing
((Xpr1 = Xpr2 ∈ (Id ⟶ hdataflow(Info;B))) and
(Ypr1 = Ypr2 ∈ (Id ⟶ hdataflow(Info;B))))
supposing valueall-type(B)
Proof
Definitions occuring in Statement :
parallel-class-program: X || Y,
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
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,
squash: ↓T,
local-class: LocalClass(X),
sq_exists: ∃x:{A| B[x]},
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
prop: ℙ
Latex:
\mforall{}[Info,B:Type].
\mforall{}[X,Y:EClass(B)]. \mforall{}[Xpr1,Xpr2:LocalClass(X)]. \mforall{}[Ypr1,Ypr2:LocalClass(Y)].
(Xpr1 || Ypr1 = Xpr2 || Ypr2) supposing ((Xpr1 = Xpr2) and (Ypr1 = Ypr2))
supposing valueall-type(B)
Date html generated:
2016_05_17-AM-09_08_51
Last ObjectModification:
2016_01_17-PM-09_14_15
Theory : local!classes
Home
Index