Nuprl Lemma : parallel-eclass2-left
∀[Info,B,C:Type]. ∀[X1,X2:EClass(B ⟶ bag(C))]. ∀[X:EClass(B)]. ((X1 o X) || (X2 o X) = (X1 || X2 o X) ∈ 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]),
class-ap: X(e),
eclass-compose2: eclass-compose2(f;X;Y),
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
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
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X1,X2:EClass(B {}\mrightarrow{} bag(C))]. \mforall{}[X:EClass(B)].
((X1 o X) || (X2 o X) = (X1 || X2 o X))
Date html generated:
2016_05_16-PM-02_28_58
Last ObjectModification:
2015_12_29-AM-11_39_07
Theory : event-ordering
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