Nuprl Lemma : disjoint-union-comb-disjoint-classrel
∀[Info,A,B,C:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[Z:EClass(C)].
(disjoint-classrel(es;B;Y;C;Z) ⇒ disjoint-classrel(es;A;X;C;Z) ⇒ disjoint-classrel(es;A + B;X (+) Y;C;Z))
Proof
Definitions occuring in Statement :
disjoint-union-comb: 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,
union: left + right,
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,
outl: outl(x),
isl: isl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
outr: outr(x),
true: True,
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,C:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[Z:EClass(C)].
(disjoint-classrel(es;B;Y;C;Z)
{}\mRightarrow{} disjoint-classrel(es;A;X;C;Z)
{}\mRightarrow{} disjoint-classrel(es;A + B;X (+) Y;C;Z))
Date html generated:
2016_05_17-AM-09_34_31
Last ObjectModification:
2015_12_29-PM-03_59_40
Theory : classrel!lemmas
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