Nuprl Lemma : Memory-class-trans2
[Info,B,A:Type].
R:B 
B 
. f:A B B. init:Id bag(B). X:EClass(A). es:EO+(Info). e1,e2:E. v1,v2:B.
(Trans(B;x,y.R[x;y])
(s1,s2:B. SqStable(R[s1;s2]))
(a:A. e:E. (e1 
loc e (e <loc e2) a 
X(e) (s:B. (s Memory-class(f;init;X)(e) R[s;f a s]))))
single-valued-classrel(es;X;A)
single-valued-bag(init loc(e1);B)
v1 Memory-class(f;init;X)(e1)
v2 Memory-class(f;init;X)(e2)
(e1 <loc e2)
(e:E. (e1 loc e (e <loc e2) (a:A. (
a X(e)))))
(v1 = v2))
Proof not projected
Definitions occuring in Statement :
Memory-class: Memory-class(f;init;X),
single-valued-classrel: single-valued-classrel(es;X;T),
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e loc e' ,
es-locl: (e <loc e'),
es-loc: loc(e),
es-E: E,
Id: Id,
trans: Trans(T;x,y.E[x; y]),
sq_stable: SqStable(P),
uall: [x:A]. B[x],
prop: ,
so_apply: x[s1;s2],
all: x:A. B[x],
not: A,
implies: P Q,
apply: f a,
function: x:A B[x],
universe: Type,
equal: s = t,
single-valued-bag: single-valued-bag(b;T),
bag: bag(T)
Definitions :
so_lambda: 
x y.t[x; y],
so_lambda: x.t[x],
member: t T,
so_apply: x[s1;s2],
implies: P Q,
prop: ,
all: x:A. B[x],
uall: [x:A]. B[x],
false: False,
true: True,
btrue: tt,
ifthenelse: if b then t else f fi ,
and: P 
Q,
exists: 
x:A. B[x],
squash: 
T,
ycomb: Y,
guard: {T},
or: P 
Q,
iterated_classrel: iterated_classrel(es;S;A;f;init;X;e;v),
not: A,
es-le: e loc e' ,
bfalse: ff,
cand: A c B,
assert: 
b,
es-locl: (e <loc e'),
label: ...$L... t,
iff: P 
Q,
rev_implies: P Q,
uimplies: b supposing a,
so_apply: x[s],
sq_type: SQType(T),
subtype: S 
T,
!hyp_hide: x
Lemmas :
assert_elim,
es-locl-first,
bag_wf,
Id_wf,
eclass_wf,
event-ordering+_wf,
trans_wf,
sq_stable_wf,
single-valued-classrel_wf,
es-loc_wf,
single-valued-bag_wf,
Memory-class_wf,
classrel_wf,
not_wf,
es-locl_wf,
es-le_wf,
event-ordering+_inc,
es-E_wf,
all_wf,
btrue_neq_bfalse,
Memory-classrel,
es-first_wf,
or_wf,
bag-member_wf,
equal_wf,
and_wf,
exists_wf,
bool_subtype_base,
bool_wf,
subtype_base_sq,
es-pred_property,
iterated_classrel-single-val,
iterated_classrel_wf,
true_wf,
squash_wf,
es-causl_wf,
not_assert_elim,
false_wf,
assert_wf,
es-causle_weakening,
es-causl_transitivity2,
es-causl_weakening,
es-causle_weakening_locl,
es-pred-causl,
es-le_weakening,
es-pred-locl,
es-pred-le,
es-pred_wf,
iterated_classrel_trans3,
es-causle_wf,
es-causl_irreflexivity,
es-causle_weakening_eq,
es-locl-trichotomy,
es-loc-pred,
es-locl_transitivity1,
es-locl_irreflexivity,
es-le_weakening_eq,
es-locl_transitivity2
\mforall{}[Info,B,A:Type].
\mforall{}R:B {}\mrightarrow{} B {}\mrightarrow{} \mBbbP{}. \mforall{}f:A {}\mrightarrow{} B {}\mrightarrow{} B. \mforall{}init:Id {}\mrightarrow{} bag(B). \mforall{}X:EClass(A). \mforall{}es:EO+(Info). \mforall{}e1,e2:E.
\mforall{}v1,v2:B.
(Trans(B;x,y.R[x;y])
{}\mRightarrow{} (\mforall{}s1,s2:B. SqStable(R[s1;s2]))
{}\mRightarrow{} (\mforall{}a:A. \mforall{}e:E.
(e1 \mleq{}loc e
{}\mRightarrow{} (e <loc e2)
{}\mRightarrow{} a \mmember{} X(e)
{}\mRightarrow{} (\mforall{}s:B. (s \mmember{} Memory-class(f;init;X)(e) {}\mRightarrow{} R[s;f a s]))))
{}\mRightarrow{} single-valued-classrel(es;X;A)
{}\mRightarrow{} single-valued-bag(init loc(e1);B)
{}\mRightarrow{} v1 \mmember{} Memory-class(f;init;X)(e1)
{}\mRightarrow{} v2 \mmember{} Memory-class(f;init;X)(e2)
{}\mRightarrow{} (e1 <loc e2)
{}\mRightarrow{} (\mforall{}e:E. (e1 \mleq{}loc e {}\mRightarrow{} (e <loc e2) {}\mRightarrow{} (\mforall{}a:A. (\mneg{}a \mmember{} X(e)))))
{}\mRightarrow{} (v1 = v2))
Date html generated:
2012_02_20-PM-02_54_08
Last ObjectModification:
2012_01_29-PM-07_59_14
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