Nuprl Lemma : loop-class-state-single-val
∀[Info,B:Type]. ∀[init:Id ⟶ bag(B)]. ∀[X:EClass(B ⟶ B)]. ∀[es:EO+(Info)].
  (single-valued-classrel(es;loop-class-state(X;init);B)) supposing 
     ((∀l:Id. single-valued-bag(init l;B)) and 
     single-valued-classrel(es;X;B ⟶ B))
Proof
Definitions occuring in Statement : 
loop-class-state: loop-class-state(X;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
, 
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]
, 
member: t ∈ T
, 
subtype_rel: A ⊆r B
, 
strongwellfounded: SWellFounded(R[x; y])
, 
exists: ∃x:A. B[x]
, 
uall: ∀[x:A]. B[x]
, 
nat: ℕ
, 
implies: P 
⇒ Q
, 
false: False
, 
ge: i ≥ j 
, 
uimplies: b supposing a
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
not: ¬A
, 
top: Top
, 
and: P ∧ Q
, 
prop: ℙ
, 
guard: {T}
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
less_than: a < b
, 
squash: ↓T
, 
uiff: uiff(P;Q)
, 
sq_type: SQType(T)
, 
ifthenelse: if b then t else f fi 
, 
btrue: tt
, 
single-valued-bag: single-valued-bag(b;T)
, 
bfalse: ff
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,B:Type].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].  \mforall{}[X:EClass(B  {}\mrightarrow{}  B)].  \mforall{}[es:EO+(Info)].
    (single-valued-classrel(es;loop-class-state(X;init);B))  supposing 
          ((\mforall{}l:Id.  single-valued-bag(init  l;B))  and 
          single-valued-classrel(es;X;B  {}\mrightarrow{}  B))
Date html generated:
2016_05_16-PM-11_36_04
Last ObjectModification:
2016_01_17-PM-07_06_00
Theory : event-ordering
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