{ 
es:EO
[T:Type]
i:Id
[P:T 
]. [Q:E T ].
((x:T. Dec(P[x]))
(L:T List
(x
L.P[x] (
e:E. Q[e;x]))
e'@i.True supposing 
(xL. P[x])
e'@i.(xL.P[x] (e:E. (e 
loc e' 
Q[e;x])))
supposing (xL.e:E. (Q[e;x] (loc(e) = i))))) }
{ Proof }
Definitions occuring in Statement :
existse-at: e@i.P[e],
es-le: e loc e' ,
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
decidable: Dec(P),
uimplies: b supposing a,
uall: [x:A]. B[x],
prop: ,
so_apply: x[s1;s2],
so_apply: x[s],
all: x:A. B[x],
exists: x:A. B[x],
not: A,
implies: P Q,
and: P Q,
true: True,
function: x:A B[x],
list: type List,
universe: Type,
equal: s = t,
l_exists: (xL. P[x]),
l_all: (xL.P[x])
Definitions :
guard: {T},
rev_implies: P 
Q,
iff: P Q,
tl: tl(l),
hd: hd(l),
cons: [car / cdr],
pair: <a, b>,
bool: 
,
top: Top,
select: l[i],
natural_number: $n,
label: ...$L... t,
int: 
,
length: ||as||,
void: Void,
cand: A c B,
nat: 
,
false: False,
limited-type: LimitedType,
set: {x:A| B[x]} ,
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
less_than: a < b,
uiff: uiff(P;Q),
union: left + right,
or: P 
Q,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
infix_ap: x f y,
atom: Atom$n,
dep-isect: Error :dep-isect,
record+: record+,
subtype_rel: A 
r B,
nil: [],
axiom: Ax,
es-loc: loc(e),
l_member: (x l),
lambda: 
x.A[x],
record-select: r.x,
member: t T,
event_ordering: EO,
universe: Type,
prop: ,
decidable: Dec(P),
list: type List,
Id: Id,
equal: s = t,
uall: [x:A]. B[x],
all: x:A. B[x],
implies: P Q,
function: x:A B[x],
exists: x:A. B[x],
and: P Q,
product: x:A 
B[x],
so_apply: x[s1;s2],
es-le: e loc e' ,
es-E: E,
uimplies: b supposing a,
isect: 
x:A. B[x],
existse-at: e@i.P[e],
true: True,
not: A,
l_exists: (xL. P[x]),
so_lambda: 
x.t[x],
so_apply: x[s],
apply: f a,
l_all: (xL.P[x]),
CollapseTHEN: Error :CollapseTHEN,
RepeatFor: Error :RepeatFor,
CollapseTHENM: Error :CollapseTHENM,
CollapseTHENA: Error :CollapseTHENA,
Try: Error :Try,
Repeat: Error :Repeat,
MaAuto: Error :MaAuto,
D: Error :D,
THENM: Error :THENM,
Complete: Error :Complete,
tactic: Error :tactic,
sqequal: s ~ t,
p-outcome: Outcome,
add: n + m,
lelt: i j < k,
real: 
,
rationals: 
,
subtype: S T,
int_seg: {i..j
},
es-locl: (e <loc e'),
trans: Trans(T;x,y.E[x; y]),
assert: 
b
Lemmas :
not_functionality_wrt_iff,
l_exists_cons,
es-le-trans,
es-locl_wf,
es-le-total,
le_wf,
member_wf,
nat_wf,
select_member,
length_wf1,
non_neg_length,
l_all_wf,
es-E_wf,
es-le_wf,
Id_wf,
uall_wf,
decidable_wf,
not_wf,
l_exists_wf,
existse-at_wf,
true_wf,
event_ordering_wf,
l_member_wf,
es-loc_wf,
l_all_wf2,
false_wf,
length_wf_nat,
length_nil,
top_wf,
l_all_nil,
cons_member
\mforall{}es:EO
\mforall{}[T:Type]
\mforall{}i:Id
\mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. \mforall{}[Q:E {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}].
((\mforall{}x:T. Dec(P[x]))
{}\mRightarrow{} (\mforall{}L:T List
(\mforall{}x\mmember{}L.P[x] {}\mRightarrow{} (\mexists{}e:E. Q[e;x]))
{}\mRightarrow{} \mexists{}e'@i.True supposing \mneg{}(\mexists{}x\mmember{}L. P[x])
{}\mRightarrow{} \mexists{}e'@i.(\mforall{}x\mmember{}L.P[x] {}\mRightarrow{} (\mexists{}e:E. (e \mleq{}loc e' \mwedge{} Q[e;x])))
supposing (\mforall{}x\mmember{}L.\mforall{}e:E. (Q[e;x] {}\mRightarrow{} (loc(e) = i)))))
Date html generated:
2011_08_16-AM-10_51_36
Last ObjectModification:
2011_06_18-AM-09_26_28
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