Nuprl Lemma : decidable__alle-lt
es:EO. e':E. [P:{e:E| loc(e) = loc(e')} 
]. (e@loc(e').Dec(P[e]) 
Dec(e<e'.P[e]))
Proof not projected
Definitions occuring in Statement :
alle-lt: e<e'.P[e],
alle-at: e@i.P[e],
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
decidable: Dec(P),
uall: [x:A]. B[x],
prop: ,
so_apply: x[s],
all: x:A. B[x],
implies: P Q,
set: {x:A| B[x]} ,
function: x:A B[x],
equal: s = t
Definitions :
so_lambda: 
x.t[x],
member: t 
T,
so_apply: x[s],
implies: P Q,
prop: ,
uall: [x:A]. B[x],
all: x:A. B[x],
cand: A c
B,
and: P Q,
uimplies: b supposing a,
bfalse: ff,
ifthenelse: if b then t else f fi ,
btrue: tt,
assert: 
b,
false: False,
or: P 
Q,
true: True,
not: 
A,
decidable: Dec(P),
suptype: suptype(S; T),
subtype: S 
T,
alle-at: e@i.P[e],
guard: {T},
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
iff: P 
Q,
rev_implies: P Q,
uiff: uiff(P;Q),
unit: Unit,
bool: 
,
it: 
Lemmas :
event_ordering_wf,
es-locl_wf,
es-E_wf,
all_wf,
alle-lt_wf,
decidable_wf,
alle-at_wf,
es-loc_wf,
Id_wf,
uall_wf,
event_system-level-subtype,
es-locl-wellfnd,
es-loc-pred,
alle-lt-iff,
es-pred_wf,
es-first_wf,
assert_wf,
not_wf,
decidable_functionality,
assert_of_bnot,
eqff_to_assert,
bnot_wf,
equal_wf,
uiff_transitivity,
eqtt_to_assert,
bool_wf,
true_wf,
es-pred-locl
\mforall{}es:EO. \mforall{}e':E. \mforall{}[P:\{e:E| loc(e) = loc(e')\} {}\mrightarrow{} \mBbbP{}]. (\mforall{}e@loc(e').Dec(P[e]) {}\mRightarrow{} Dec(\mforall{}e<e'.P[e]))
Date html generated:
2012_01_23-PM-12_14_01
Last ObjectModification:
2011_12_13-AM-10_30_36
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