Nuprl Lemma : parallel-class-es-sv
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[X,Y:EClass(A)].
(es-sv-class(es;X || Y)) supposing (es-sv-class(es;X) and es-sv-class(es;Y) and disjoint-classrel(es;A;X;A;Y))
Proof
Definitions occuring in Statement :
parallel-class: X || Y,
es-sv-class: es-sv-class(es;X),
disjoint-classrel: disjoint-classrel(es;A;X;B;Y),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
parallel-class: X || Y,
es-sv-class: es-sv-class(es;X),
eclass-compose2: eclass-compose2(f;X;Y),
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
eclass: EClass(A[eo; e]),
subtype_rel: A ⊆r B,
nat: ℕ,
implies: P ⇒ Q,
decidable: Dec(P),
or: P ∨ Q,
guard: {T},
prop: ℙ,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
and: P ∧ Q,
cand: A c∧ B,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
classrel: v ∈ X(e),
disjoint-classrel: disjoint-classrel(es;A;X;B;Y),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
le: A ≤ B
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X,Y:EClass(A)].
(es-sv-class(es;X || Y)) supposing
(es-sv-class(es;X) and
es-sv-class(es;Y) and
disjoint-classrel(es;A;X;A;Y))
Date html generated:
2016_05_17-AM-09_31_03
Last ObjectModification:
2016_01_17-PM-11_09_10
Theory : classrel!lemmas
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