Nuprl Lemma : member-disjoint-union-comb-bool
∀[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. (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,
uall: ∀[x:A]. B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
false: False,
not: ¬A,
prop: ℙ,
rev_implies: P ⇐ Q,
true: True,
guard: {T},
sq_type: SQType(T),
rev_uimplies: rev_uimplies(P;Q),
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
(e \mmember{}\msubb{} X (+) Y \msim{} e \mmember{}\msubb{} X \mvee{}\msubb{}e \mmember{}\msubb{} Y)
Date html generated:
2016_05_17-AM-11_12_47
Last ObjectModification:
2015_12_29-PM-05_15_04
Theory : process-model
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