Nuprl Lemma : State-class-es-sv
∀[Info,A:Type]. ∀[es:EO+(Info)]. ∀[f:Top]. ∀[X:EClass(A)]. ∀[init:Id ⟶ bag(Top)].
  (es-sv-class(es;State-class(init;f;X))) supposing ((∀l:Id. (#(init l) ≤ 1)) and es-sv-class(es;X))
Proof
Definitions occuring in Statement : 
State-class: State-class(init;f;X)
, 
es-sv-class: es-sv-class(es;X)
, 
eclass: EClass(A[eo; e])
, 
event-ordering+: EO+(Info)
, 
Id: Id
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
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 : 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
, 
nat: ℕ
, 
so_apply: x[s]
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
uimplies: b supposing a
, 
es-sv-class: es-sv-class(es;X)
, 
all: ∀x:A. B[x]
, 
le: A ≤ B
, 
and: P ∧ Q
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
false: False
, 
State-class: State-class(init;f;X)
, 
simple-comb-2: F|X, Y|
, 
simple-comb: simple-comb(F;Xs)
, 
select: L[n]
, 
cons: [a / b]
, 
subtract: n - m
, 
eclass: EClass(A[eo; e])
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
uiff: uiff(P;Q)
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
lifting-2: lifting-2(f)
, 
lifting2: lifting2(f;abag;bbag)
, 
lifting-gen-rev: lifting-gen-rev(n;f;bags)
, 
lifting-gen-list-rev: lifting-gen-list-rev(n;bags)
, 
eq_int: (i =z j)
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
guard: {T}
, 
ge: i ≥ j 
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
less_than': less_than'(a;b)
, 
single-bag: {x}
, 
empty-bag: {}
, 
bag-size: #(bs)
Latex:
\mforall{}[Info,A:Type].  \mforall{}[es:EO+(Info)].  \mforall{}[f:Top].  \mforall{}[X:EClass(A)].  \mforall{}[init:Id  {}\mrightarrow{}  bag(Top)].
    (es-sv-class(es;State-class(init;f;X)))  supposing  ((\mforall{}l:Id.  (\#(init  l)  \mleq{}  1))  and  es-sv-class(es;X))
Date html generated:
2016_05_17-AM-09_36_27
Last ObjectModification:
2016_01_17-PM-11_07_35
Theory : classrel!lemmas
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