Nuprl Lemma : mem_test_ord_max
es:EO'. e1,e2:E. n1,n2:
. ((e1 <loc e2) 
n1 
mem_test_Maximum()(e1) n2 mem_test_Maximum()(e2) (n1 
n2))
Proof not projected
Definitions occuring in Statement :
mem_test_Maximum: mem_test_Maximum(),
Message: Message,
classrel: v X(e),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
le: A B,
all: x:A. B[x],
implies: P Q,
int:
Definitions :
all: x:A. B[x],
implies: P Q,
le: A B,
mem_test_int'base: mem_test_int'base(),
prop: 
,
refl: Refl(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
member: t T,
so_lambda: 
x.t[x],
not: 
A,
false: False,
or: P 
Q,
assert: 
b,
bfalse: ff,
ifthenelse: if b then t else f fi ,
name: Name,
mem_test_Maximum: mem_test_Maximum(),
uall: [x:A]. B[x],
so_apply: x[s1;s2],
iff: P 
Q,
and: P 
Q,
rev_implies: P Q,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
subtype: S 
T
Lemmas :
State-comb-trans-refl,
Message_wf,
le_wf,
imax_wf,
single-bag_wf,
Id_wf,
mem_test_int'base_wf,
sq_stable_from_decidable,
decidable__le,
imax_ub,
classrel_wf,
State-comb_wf,
es-pred_wf,
event-ordering+_inc,
subtype_base_sq,
bool_subtype_base,
false_wf,
es-le_wf,
es-locl_wf,
single-valued-classrel-base,
single-valued-bag-single,
es-le_weakening,
mem_test_Maximum_wf,
es-E_wf,
event-ordering+_wf,
es-locl-first
\mforall{}es:EO'. \mforall{}e1,e2:E. \mforall{}n1,n2:\mBbbZ{}.
((e1 <loc e2) {}\mRightarrow{} n1 \mmember{} mem\_test\_Maximum()(e1) {}\mRightarrow{} n2 \mmember{} mem\_test\_Maximum()(e2) {}\mRightarrow{} (n1 \mleq{} n2))
Date html generated:
2012_02_20-PM-05_12_04
Last ObjectModification:
2012_02_17-PM-06_28_39
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