Nuprl Lemma : eclass0-single-val
∀[Info,B,C:Type]. ∀[X:EClass(B)]. ∀[f:Id ⟶ B ⟶ bag(C)]. ∀[es:EO+(Info)].
  (single-valued-classrel(es;(f o X);C)) supposing 
     (single-valued-classrel(es;X;B) and 
     (∀i:Id. ∀b:B.  single-valued-bag(f i b;C)))
Proof
Definitions occuring in Statement : 
eclass0: (f o X)
, 
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
, 
single-valued-bag: single-valued-bag(b;T)
, 
bag: bag(T)
Definitions unfolded in proof : 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
uimplies: b supposing a
, 
single-valued-classrel: single-valued-classrel(es;X;T)
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
squash: ↓T
, 
exists: ∃x:A. B[x]
, 
classrel: v ∈ X(e)
, 
single-valued-bag: single-valued-bag(b;T)
Latex:
\mforall{}[Info,B,C:Type].  \mforall{}[X:EClass(B)].  \mforall{}[f:Id  {}\mrightarrow{}  B  {}\mrightarrow{}  bag(C)].  \mforall{}[es:EO+(Info)].
    (single-valued-classrel(es;(f  o  X);C))  supposing 
          (single-valued-classrel(es;X;B)  and 
          (\mforall{}i:Id.  \mforall{}b:B.    single-valued-bag(f  i  b;C)))
Date html generated:
2016_05_16-PM-02_09_14
Last ObjectModification:
2015_12_29-PM-02_27_35
Theory : event-ordering
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