Nuprl Lemma : State-comb-exists
[Info,B,A:Type]. [f:A 
B B]. [init:Id bag(B)].
X:EClass(A). [es:EO+(Info)]. [e:E]. 
v:B. v 
State-comb(init;f;X)(e) supposing bag-size(init loc(e)) > 0
Proof not projected
Definitions occuring in Statement :
State-comb: State-comb(init;f;X),
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uimplies: b supposing a,
uall: [x:A]. B[x],
gt: i > j,
all: x:A. B[x],
exists: x:A. B[x],
squash: T,
apply: f a,
function: x:A B[x],
natural_number: $n,
universe: Type,
bag-size: bag-size(bs),
bag: bag(T)
Definitions :
so_lambda: 
x y.t[x; y],
true: True,
false: False,
not: 
A,
le: A 
B,
ge: i 
j ,
nat: 
,
member: t T,
all: x:A. B[x],
implies: P 
Q,
squash: T,
gt: i > j,
eclass: EClass(A[eo; e]),
guard: {T},
btrue: tt,
bfalse: ff,
lt_int: i <z j,
bnot: 
b,
le_int: i z j,
select: l[i],
simple-comb: simple-comb(F;Xs),
top: Top,
simple-comb-2: F|X, Y|,
ifthenelse: if b then t else f fi ,
State-comb: State-comb(init;f;X),
classrel: v X(e),
exists: x:A. B[x],
so_lambda: x.t[x],
and: P 
Q,
or: P 
Q,
prop: 
,
es-p-local-pred: es-p-local-pred(es;P),
so_apply: x[s1;s2],
decidable: Dec(P),
uall: [x:A]. B[x],
strongwellfounded: SWellFounded(R[x; y]),
uimplies: b supposing a,
uiff: uiff(P;Q),
unit: Unit,
bool: 
,
so_apply: x[s],
rev_uimplies: rev_uimplies(P;Q),
es-locl: (e <loc e'),
subtype: S 
T,
it: 
Lemmas :
bag_wf,
Id_wf,
eclass_wf,
event-ordering+_wf,
es-E_wf,
es-loc_wf,
bag-size_wf,
gt_wf,
equal_wf,
event-ordering+_inc,
es-first_wf,
decidable__assert,
es-causl_wf,
le_wf,
nat_wf,
less_than_wf,
ge_wf,
nat_properties,
es-causl-swellfnd,
bag-member-iff-size,
not_functionality_wrt_uiff,
assert_of_bnot,
eqff_to_assert,
assert-bag-null,
eqtt_to_assert,
uiff_transitivity,
not_wf,
bnot_wf,
empty-bag_wf,
assert_wf,
bool_wf,
bag-null_wf,
State-comb_wf,
classrel_wf,
rec-combined-class-opt-1-classrel,
assert_elim,
es-locl-first,
squash_wf,
es-p-local-pred_wf,
and_wf,
exists_wf,
es-locl_wf,
btrue_neq_bfalse,
primed-class-opt-classrel,
empty-bag-iff-size,
bag-member-empty-iff,
bag-member_wf,
primed-class-opt_wf,
bag-member-lifting-2,
es-loc-pred,
es-pred-causl,
es-pred_wf,
all_wf,
es-pred-locl,
es-causl_irreflexivity,
es-causle_weakening,
es-causl_weakening,
es-causl_transitivity2,
es-locl_irreflexivity,
es-le_weakening_eq,
es-locl_transitivity2,
es-pred_property
\mforall{}[Info,B,A:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
\mforall{}X:EClass(A)
\mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mdownarrow{}\mexists{}v:B. v \mmember{} State-comb(init;f;X)(e) supposing bag-size(init loc(e)) > 0
Date html generated:
2012_02_20-PM-03_05_37
Last ObjectModification:
2012_02_07-PM-11_24_51
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