Nuprl Lemma : parallel-eclass2-right
∀[Info,B,C:Type]. ∀[X:EClass(B ⟶ bag(C))]. ∀[X1,X2:EClass(B)]. ((X o X1) || (X o X2) = (X o X1 || X2) ∈ EClass(C))
Proof
Definitions occuring in Statement :
parallel-class: X || Y,
eclass2: (X o Y),
eclass: EClass(A[eo; e]),
uall: ∀[x:A]. B[x],
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,
parallel-class: X || Y,
eclass2: (X o Y),
eclass: EClass(A[eo; e]),
eclass-compose2: eclass-compose2(f;X;Y),
class-ap: X(e),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} bag(C))]. \mforall{}[X1,X2:EClass(B)].
((X o X1) || (X o X2) = (X o X1 || X2))
Date html generated:
2016_05_16-PM-02_29_10
Last ObjectModification:
2016_01_17-PM-07_32_41
Theory : event-ordering
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