Nuprl Lemma : parallel-class-single-val
∀[Info,A:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(A)].
(single-valued-classrel(es;X || Y;A)) supposing
(single-valued-classrel(es;X;A) and
single-valued-classrel(es;Y;A) and
disjoint-classrel(es;A;X;A;Y))
Proof
Definitions occuring in Statement :
parallel-class: X || Y,
single-valued-classrel: single-valued-classrel(es;X;T),
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 :
single-valued-classrel: single-valued-classrel(es;X;T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
sq_or: a ↓∨ b,
squash: ↓T,
or: P ∨ Q,
disjoint-classrel: disjoint-classrel(es;A;X;B;Y),
not: ¬A,
false: False,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(A)].
(single-valued-classrel(es;X || Y;A)) supposing
(single-valued-classrel(es;X;A) and
single-valued-classrel(es;Y;A) and
disjoint-classrel(es;A;X;A;Y))
Date html generated:
2016_05_17-AM-09_30_57
Last ObjectModification:
2015_12_29-PM-04_01_13
Theory : classrel!lemmas
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