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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