{ 
es:EO
[P:E 
]
d:e,e':E. Dec(es-p-immediate-pred(es;
e.P[e]) e e')
((e:E. Dec(P[e]))
(e:E
(P[e]
{P[final-iterate(es-r-pred{i:l}(es;d);e)]
(
(
e':E
((e' < final-iterate(es-r-pred{i:l}(es;d);e))
P[e'])))}))) }
{ Proof }
Definitions occuring in Statement :
es-p-immediate-pred: es-p-immediate-pred(es;P),
es-r-pred: es-r-pred{i:l}(es;d),
es-causl: (e < e'),
es-E: E,
event_ordering: EO,
decidable: Dec(P),
uall: [x:A]. B[x],
prop: ,
guard: {T},
so_apply: x[s],
all: x:A. B[x],
exists: x:A. B[x],
not: A,
implies: P Q,
and: P Q,
apply: f a,
lambda: x.A[x],
function: x:A B[x],
final-iterate: final-iterate(f;x)
Definitions :
assert: 
b,
cand: A c B,
nat: 
,
top: Top,
so_lambda: 
x.t[x],
record: record(x.T[x]),
strong-subtype: strong-subtype(A;B),
equal: s = t,
union: left + right,
or: P 
Q,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
infix_ap: x f y,
record-select: r.x,
dep-isect: Error :dep-isect,
record+: record+,
le: A 
B,
ge: i 
j ,
less_than: a < b,
uimplies: b supposing a,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
exists: x:A. B[x],
void: Void,
false: False,
not: A,
event_ordering: EO,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
guard: {T},
and: P Q,
product: x:A 
B[x],
universe: Type,
decidable: Dec(P),
ExRepD: Error :ExRepD,
Auto: Error :Auto,
es-r-pred: es-r-pred{i:l}(es;d),
es-E: E,
THENA: Error :THENA,
CollapseTHEN: Error :CollapseTHEN,
p-graph: p-graph(A;f),
apply: f a,
strongwellfounded: SWellFounded(R[x; y]),
AssertBY: Error :AssertBY,
RepUR: Error :RepUR,
so_apply: x[s],
lambda: x.A[x],
es-p-immediate-pred: es-p-immediate-pred(es;P),
es-causl: (e < e'),
so_apply: x[s1;s2],
implies: P Q,
all: x:A. B[x],
prop: ,
function: x:A B[x],
set: {x:A| B[x]} ,
member: t 
T,
tactic: Error :tactic,
bool: 
,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
int: 
,
subtype: S T,
suptype: suptype(S; T),
p-fun-exp: f^n,
do-apply: do-apply(f;x),
final-iterate: final-iterate(f;x),
can-apply: can-apply(f;x),
sq_type: SQType(T),
rev_implies: P 
Q,
iff: P Q,
causal-predecessor: causal-predecessor(es;p),
true: True,
fpf: a:A fp-> B[a],
list: type List,
subtract: n - m,
outl: outl(x),
p-compose: f o g,
inl: inl x ,
isl: isl(x),
axiom: Ax,
natural_number: $n,
primrec: primrec(n;b;c),
p-id: p-id(),
minus: -n,
add: n + m,
sqequal: s ~ t,
real: 
,
rationals: 
,
p-outcome: Outcome,
D: Error :D,
THENM: Error :THENM,
squash: 
T,
BHyp: Error :BHyp,
THEN: Error :THEN,
Unfold: Error :Unfold
Lemmas :
es-p-immediate-pred-exists,
squash_wf,
rev_implies_wf,
iff_wf,
p-fun-exp-add-sq,
p-fun-exp-one,
iff_weakening_uiff,
assert_functionality_wrt_uiff,
can-apply-fun-exp-add-iff,
le_wf,
nat_wf,
p-fun-exp_wf,
int_subtype_base,
ge_wf,
nat_properties,
nat_ind_tp,
true_wf,
bool_wf,
isl_wf,
assert_witness,
do-apply_wf,
es-r-pred-property,
subtype_base_sq,
assert_wf,
member_wf,
top_wf,
can-apply_wf,
final-iterate_wf,
false_wf,
guard_wf,
not_wf,
decidable_wf,
event_ordering_wf,
es-E_wf,
es-p-immediate-pred_wf,
es-causl_wf,
es-p-immediate-pred-wellfounded,
final-iterate-property,
es-r-pred_wf
\mforall{}es:EO
\mforall{}[P:E {}\mrightarrow{} \mBbbP{}]
\mforall{}d:\mforall{}e,e':E. Dec(es-p-immediate-pred(es;\mlambda{}e.P[e]) e e')
((\mforall{}e:E. Dec(P[e]))
{}\mRightarrow{} (\mforall{}e:E
(P[e]
{}\mRightarrow{} \{P[final-iterate(es-r-pred\{i:l\}(es;d);e)]
\mwedge{} (\mneg{}(\mexists{}e':E. ((e' < final-iterate(es-r-pred\{i:l\}(es;d);e)) \mwedge{} P[e'])))\})))
Date html generated:
2011_08_16-AM-11_14_08
Last ObjectModification:
2011_06_20-AM-00_21_19
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