Nuprl Lemma : rec-combined-class-opt-1-single-val
∀[Info,A,B:Type]. ∀[es:EO+(Info)]. ∀[F:A ⟶ B ⟶ B]. ∀[X:EClass(A)]. ∀[init:Id ⟶ bag(B)].
  (single-valued-classrel(es;lifting-2(F)|X,Prior(self)?init|;B)) supposing 
     (single-valued-classrel(es;X;A) and 
     (∀l:Id. single-valued-bag(init l;B)))
Proof
Definitions occuring in Statement : 
rec-combined-class-opt-1: F|X,Prior(self)?init|
, 
single-valued-classrel: single-valued-classrel(es;X;T)
, 
eclass: EClass(A[eo; e])
, 
event-ordering+: EO+(Info)
, 
Id: Id
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
apply: f a
, 
function: x:A ⟶ B[x]
, 
universe: Type
, 
lifting-2: lifting-2(f)
, 
single-valued-bag: single-valued-bag(b;T)
, 
bag: bag(T)
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
, 
uimplies: b supposing a
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
, 
guard: {T}
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A,B:Type].  \mforall{}[es:EO+(Info)].  \mforall{}[F:A  {}\mrightarrow{}  B  {}\mrightarrow{}  B].  \mforall{}[X:EClass(A)].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].
    (single-valued-classrel(es;lifting-2(F)|X,Prior(self)?init|;B))  supposing 
          (single-valued-classrel(es;X;A)  and 
          (\mforall{}l:Id.  single-valued-bag(init  l;B)))
Date html generated:
2016_05_17-AM-09_30_10
Last ObjectModification:
2015_12_29-PM-04_01_10
Theory : classrel!lemmas
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