Nuprl Lemma : State-comb-classrel-class
[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) 
v State-class(init;f;X)(e))
Proof not projected
Definitions occuring in Statement :
State-comb: State-comb(init;f;X),
State-class: State-class(init;f;X),
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
uall: [x:A]. B[x],
all: x:A. B[x],
iff: P Q,
function: x:A B[x],
universe: Type,
bag: bag(T)
Definitions :
so_lambda: 
x y.t[x; y],
rev_implies: P Q,
and: P 
Q,
true: True,
squash: 
T,
false: False,
not: 
A,
le: A 
B,
ge: i 
j ,
implies: P Q,
nat: 
,
member: t T,
all: x:A. B[x],
iff: P Q,
guard: {T},
top: Top,
eclass: EClass(A[eo; e]),
ifthenelse: if b then t else f fi ,
bfalse: ff,
assert: 
b,
so_lambda: x.t[x],
prop: 
,
ycomb: Y,
iterated_classrel: iterated_classrel(es;S;A;f;init;X;e;v),
exists: 
x:A. B[x],
btrue: tt,
or: P 
Q,
cand: A c B,
gt: i > j,
Id: Id,
lt_int: i <z j,
bnot: 
b,
le_int: i z j,
select: l[i],
simple-comb: simple-comb(F;Xs),
simple-comb-2: F|X, Y|,
State-comb: State-comb(init;f;X),
classrel: v X(e),
es-p-local-pred: es-p-local-pred(es;P),
so_apply: x[s1;s2],
uall: [x:A]. B[x],
strongwellfounded: SWellFounded(R[x; y]),
uiff: uiff(P;Q),
uimplies: b supposing a,
sq_type: SQType(T),
sq_stable: SqStable(P),
es-locl: (e <loc e'),
so_apply: x[s],
unit: Unit,
bool: 
,
rev_uimplies: rev_uimplies(P;Q),
decidable: Dec(P),
subtype: S 
T,
it: 
Lemmas :
bag_wf,
Id_wf,
eclass_wf,
event-ordering+_wf,
event-ordering+_inc,
es-E_wf,
equal_wf,
State-class_wf,
State-comb_wf,
classrel_wf,
es-causl_wf,
le_wf,
nat_wf,
less_than_wf,
ge_wf,
nat_properties,
es-causl-swellfnd,
not_functionality_wrt_uiff,
assert_of_bnot,
eqff_to_assert,
assert-bag-null,
eqtt_to_assert,
uiff_transitivity,
bool_subtype_base,
subtype_base_sq,
bool_cases,
not_wf,
bnot_wf,
empty-bag_wf,
assert_wf,
bool_wf,
bag-null_wf,
rec-combined-class-opt-1-classrel,
State-classrel,
sq_stable__iterated_classrel,
primed-class-opt-classrel,
es-loc-pred,
es-locl-first,
false_wf,
es-pred_wf,
es-locl-trichotomy,
gt_wf,
bag-size_wf,
and_wf,
State-comb-exists-iff,
State-comb-exists,
es-pred-locl,
all_wf,
exists_wf,
or_wf,
iterated_classrel_wf,
es-loc_wf,
bag-member_wf,
es-first_wf,
ifthenelse_wf,
assert_elim,
btrue_neq_bfalse,
bag-member-empty-iff,
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,
atom2_subtype_base,
bag-member-iff-size,
primed-class-opt_wf,
bag-member-lifting-2,
squash_wf,
es-p-local-pred_wf,
es-locl_wf,
es-pred-causl,
empty-bag-iff-size,
decidable__lt
\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.
\mforall{}[v:B]. (v \mmember{} State-comb(init;f;X)(e) \mLeftarrow{}{}\mRightarrow{} v \mmember{} State-class(init;f;X)(e))
Date html generated:
2012_02_20-PM-03_06_14
Last ObjectModification:
2012_02_08-AM-00_47_33
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