Nuprl Lemma : loop-class-memory-total
∀[Info,B:Type]. ∀[init:Id ⟶ bag(B)]. ∀[X:EClass(B ⟶ B)]. ∀[es:EO+(Info)].
  es-total-class(es;loop-class-memory(X;init)) supposing ∀l:Id. (1 ≤ #(init l))
Proof
Definitions occuring in Statement : 
loop-class-memory: loop-class-memory(X;init)
, 
es-total-class: es-total-class(es;X)
, 
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
, 
bag-size: #(bs)
, 
bag: bag(T)
Definitions unfolded in proof : 
es-total-class: es-total-class(es;X)
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
subtype_rel: A ⊆r B
, 
nat: ℕ
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
le: A ≤ B
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
top: Top
, 
prop: ℙ
, 
uiff: uiff(P;Q)
, 
classrel: v ∈ X(e)
, 
class-ap: X(e)
, 
eclass: EClass(A[eo; e])
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
less_than: a < b
, 
squash: ↓T
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Latex:
\mforall{}[Info,B:Type].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].  \mforall{}[X:EClass(B  {}\mrightarrow{}  B)].  \mforall{}[es:EO+(Info)].
    es-total-class(es;loop-class-memory(X;init))  supposing  \mforall{}l:Id.  (1  \mleq{}  \#(init  l))
Date html generated:
2016_05_16-PM-11_40_45
Last ObjectModification:
2016_01_17-PM-07_03_32
Theory : event-ordering
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