Nuprl Lemma : loop-class-state-functional
∀[Info,B:Type]. ∀[init:Id ⟶ bag(B)]. ∀[X:EClass(B ⟶ B)]. ∀[es:EO+(Info)].
  (loop-class-state(X;init) is functional) supposing 
     ((∀l:Id. single-valued-bag(init l;B)) and 
     single-valued-classrel(es;X;B ⟶ B) and 
     (∀l:Id. (1 ≤ #(init l))))
Proof
Definitions occuring in Statement : 
loop-class-state: loop-class-state(X;init)
, 
es-functional-class: X is functional
, 
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]
, 
le: A ≤ B
, 
all: ∀x:A. B[x]
, 
apply: f a
, 
function: x:A ⟶ B[x]
, 
natural_number: $n
, 
universe: Type
, 
single-valued-bag: single-valued-bag(b;T)
, 
bag-size: #(bs)
, 
bag: bag(T)
Definitions unfolded in proof : 
es-functional-class: X is functional
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
, 
nat: ℕ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
single-valued-classrel: single-valued-classrel(es;X;T)
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
es-total-class: es-total-class(es;X)
, 
le: A ≤ B
, 
not: ¬A
, 
false: False
Latex:
\mforall{}[Info,B:Type].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].  \mforall{}[X:EClass(B  {}\mrightarrow{}  B)].  \mforall{}[es:EO+(Info)].
    (loop-class-state(X;init)  is  functional)  supposing 
          ((\mforall{}l:Id.  single-valued-bag(init  l;B))  and 
          single-valued-classrel(es;X;B  {}\mrightarrow{}  B)  and 
          (\mforall{}l:Id.  (1  \mleq{}  \#(init  l))))
Date html generated:
2016_05_16-PM-11_36_20
Last ObjectModification:
2015_12_29-AM-10_12_25
Theory : event-ordering
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