Nuprl Lemma : member-disjoint-union-comb
∀[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E].  uiff(↑e ∈b X (+) Y;↑(e ∈b X ∨be ∈b Y))
Proof
Definitions occuring in Statement : 
disjoint-union-comb: X (+) Y
, 
member-eclass: e ∈b X
, 
eclass: EClass(A[eo; e])
, 
event-ordering+: EO+(Info)
, 
es-E: E
, 
bor: p ∨bq
, 
assert: ↑b
, 
uiff: uiff(P;Q)
, 
uall: ∀[x:A]. B[x]
, 
universe: Type
Definitions unfolded in proof : 
member-eclass: e ∈b X
, 
disjoint-union-comb: X (+) Y
, 
parallel-class: X || Y
, 
eclass-compose2: eclass-compose2(f;X;Y)
, 
lifting-1: lifting-1(f)
, 
lifting1: lifting1(f;b)
, 
lifting-gen-rev: lifting-gen-rev(n;f;bags)
, 
lifting-gen-list-rev: lifting-gen-list-rev(n;bags)
, 
eq_int: (i =z j)
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
btrue: tt
, 
simple-comb-1: F|X|
, 
simple-comb: simple-comb(F;Xs)
, 
select: L[n]
, 
cons: [a / b]
, 
top: Top
, 
member: t ∈ T
, 
class-ap: X(e)
, 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
subtype_rel: A ⊆r B
, 
nat: ℕ
, 
implies: P 
⇒ Q
, 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
not: ¬A
, 
prop: ℙ
, 
rev_implies: P 
⇐ Q
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
guard: {T}
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
ge: i ≥ j 
Latex:
\mforall{}[Info,A,B:Type].  \mforall{}[X:EClass(A)].  \mforall{}[Y:EClass(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].
    uiff(\muparrow{}e  \mmember{}\msubb{}  X  (+)  Y;\muparrow{}(e  \mmember{}\msubb{}  X  \mvee{}\msubb{}e  \mmember{}\msubb{}  Y))
Date html generated:
2016_05_17-AM-11_12_42
Last ObjectModification:
2016_01_18-AM-00_10_22
Theory : process-model
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