Nuprl Lemma : State-comb-es-sv1
[Info,A,B:Type]. [es:EO+(Info)]. [f:A 
B B]. [X:EClass(A)]. [init:Id bag(B)].
(es-sv-class(es;State-comb(init;f;X))) supposing ((l:Id. (bag-size(init l) 
1)) and es-sv-class(es;X))
Proof not projected
Definitions occuring in Statement :
State-comb: State-comb(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],
le: A B,
all: x:A. B[x],
apply: f a,
function: x:A B[x],
natural_number: $n,
universe: Type,
bag-size: bag-size(bs),
bag: bag(T)
Definitions :
all: x:A. B[x],
le: A B,
State-comb: State-comb(init;f;X),
rec-combined-class-opt-1: F|X,Prior(self)?init|,
ifthenelse: if b then t else f fi ,
lifting-2: lifting-2(f),
select: l[i],
nat: 
,
int_seg: {i..j
},
implies: P 
Q,
member: t 
T,
not: 
A,
false: False,
length: ||as||,
so_lambda: 
x y.t[x; y],
lelt: i j < k,
and: P 
Q,
ycomb: Y,
le_int: i z j,
bnot: 
b,
lt_int: i <z j,
bfalse: ff,
btrue: tt,
so_lambda: x.t[x],
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 =
j),
guard: {T},
uall: [x:A]. B[x],
uimplies: b supposing a,
prop: 
,
so_apply: x[s1;s2],
decidable: Dec(P),
or: P 
Q,
sq_type: SQType(T),
so_apply: x[s],
bool: 
,
unit: Unit,
uiff: uiff(P;Q),
eclass: EClass(A[eo; e]),
subtype: S 
T,
it: 
Lemmas :
bag-size-zero,
bag-size-one,
bag-combine-single-left,
bag-combine_wf,
single-bag_wf,
bag-only_wf2,
single-valued-bag-if-le1,
rec-comb-es-sv,
le_wf,
int_seg_wf,
select_wf,
eclass_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
ifthenelse_wf,
bag-null_wf,
lelt_wf,
bag_wf,
lifting-2_wf,
Id_wf,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
bag-size_wf,
nat_wf,
all_wf,
bool_wf,
equal_wf,
assert_wf,
empty-bag_wf,
bnot_wf,
not_wf,
State-comb_wf,
es-sv-class_wf,
uiff_transitivity,
eqtt_to_assert,
assert-bag-null,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff
\mforall{}[Info,A,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X:EClass(A)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
(es-sv-class(es;State-comb(init;f;X))) supposing
((\mforall{}l:Id. (bag-size(init l) \mleq{} 1)) and
es-sv-class(es;X))
Date html generated:
2012_02_20-PM-03_08_56
Last ObjectModification:
2012_02_16-PM-07_02_28
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