Nuprl Lemma : parallel-class-disjoint-classrel
∀[Info,A,B:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(A)]. ∀[Z:EClass(B)].
(disjoint-classrel(es;A;X;B;Z) ⇒ disjoint-classrel(es;A;Y;B;Z) ⇒ disjoint-classrel(es;A;X || Y;B;Z))
Proof
Definitions occuring in Statement :
parallel-class: X || Y,
disjoint-classrel: disjoint-classrel(es;A;X;B;Y),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
disjoint-classrel: disjoint-classrel(es;A;X;B;Y),
all: ∀x:A. B[x],
member: t ∈ T,
or: P ∨ Q,
not: ¬A,
false: False,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
sq_or: a ↓∨ b,
squash: ↓T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(A)]. \mforall{}[Z:EClass(B)].
(disjoint-classrel(es;A;X;B;Z)
{}\mRightarrow{} disjoint-classrel(es;A;Y;B;Z)
{}\mRightarrow{} disjoint-classrel(es;A;X || Y;B;Z))
Date html generated:
2016_05_17-AM-09_34_02
Last ObjectModification:
2015_12_29-PM-03_59_47
Theory : classrel!lemmas
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