Nuprl Lemma : rotate-ring-step
T:Type. L:T List. x:T. ((||L|| > 0) 
(x = last(L)) rotate-ring(T;L;[x / firstn(||L|| - 1;L)]))
Proof not projected
Definitions occuring in Statement :
rotate-ring: rotate-ring(T;L1;L2),
firstn: firstn(n;as),
length: ||as||,
gt: i > j,
all: x:A. B[x],
implies: P Q,
cons: [car / cdr],
list: type List,
subtract: n - m,
natural_number: $n,
universe: Type,
equal: s = t,
last: last(L)
Definitions :
CollapseTHENA: Error :CollapseTHENA,
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
D: Error :D,
function: x:A 
B[x],
all: x:A. B[x],
last: last(L),
member: t 
T,
equal: s = t,
prop: 
,
universe: Type,
limited-type: LimitedType,
isect: 
x:A. B[x],
uall: [x:A]. B[x],
list: type List,
less_than: a < b,
gt: i > j,
rotate-ring: rotate-ring(T;L1;L2),
implies: P Q,
uimplies: b supposing a,
not: 
A,
false: False,
void: Void,
assert: 
b,
length: ||as||,
subtype_rel: A 
r B,
uiff: uiff(P;Q),
and: P 
Q,
product: x:A 
B[x],
natural_number: $n,
exists: 
x:A. B[x],
ifthenelse: if b then t else f fi ,
int_seg: {i..j
},
int: 
,
tactic: Error :tactic,
MaAuto: Error :MaAuto,
subtract: n - m,
firstn: firstn(n;as),
cons: [car / cdr],
ge: i 
j ,
le: A 
B,
strong-subtype: strong-subtype(A;B),
hd: hd(l),
tl: tl(l),
fpf: a:A fp-> B[a],
pair: <a, b>,
eclass: EClass(A[eo; e]),
add: n + m,
minus: -n,
int_iseg: {i...j},
subtype: S T,
rationals: 
,
real: 
,
set: {x:A| B[x]} ,
nat: 
,
top: Top,
or: P 
Q,
bool: 
,
lelt: i j < k,
lt_int: i <z j,
select: l[i],
cand: A c B,
nil: [],
intensional-universe: IType,
union: left + right,
unit: Unit,
bnot: 
b,
bor: p q,
band: p q,
bimplies: p q,
es-ble: e loc e',
es-bless: e <loc e',
es-eq-E: e = e',
eq_lnk: a = b,
eq_id: a = b,
name_eq: name_eq(x;y),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-member: deq-member(eq;x;L),
q_le: q_le(r;s),
q_less: q_less(r;s),
qeq: qeq(r;s),
eq_atom: eq_atom$n(x;y),
eq_type: eq_type(T;T'),
b-exists: (i<n.P[i])_b,
bl-exists: (xL.P[x])_b,
bl-all: (xL.P[x])_b,
dcdr-to-bool: [d],
infix_ap: x f y,
apply: f a,
grp_blt: a < b,
set_blt: a < b,
null: null(as),
eq_atom: x =a y,
eq_int: (i =
j),
le_int: i z j,
btrue: tt,
bfalse: ff,
l_member: (x l),
guard: {T},
so_apply: x[s],
sqequal: s ~ t,
Unfold: Error :Unfold,
sq_type: SQType(T),
grp_car: |g|,
iff: P 
Q,
rev_implies: P Q
Lemmas :
int_iseg_wf,
select_firstn,
rev_implies_wf,
iff_wf,
select-cons,
bnot_of_le_int,
int_subtype_base,
subtype_base_sq,
bnot_wf,
le_int_wf,
assert_of_le_int,
bnot_of_lt_int,
assert_functionality_wrt_uiff,
eqff_to_assert,
assert_of_lt_int,
eqtt_to_assert,
uiff_transitivity,
bool_wf,
subtype_rel_wf,
intensional-universe_wf,
lt_int_wf,
select_wf,
int_seg_properties,
length_wf_nat,
top_wf,
member_wf,
firstn_wf,
le_wf,
nat_wf,
non_neg_length,
length_cons,
length_firstn,
int_seg_wf,
ifthenelse_wf,
length_wf,
gt_wf,
pos_length2,
assert_wf,
false_wf,
not_wf,
last_wf
\mforall{}T:Type. \mforall{}L:T List. \mforall{}x:T.
((||L|| > 0) {}\mRightarrow{} (x = last(L)) {}\mRightarrow{} rotate-ring(T;L;[x / firstn(||L|| - 1;L)]))
Date html generated:
2012_02_20-PM-05_54_35
Last ObjectModification:
2012_02_02-PM-02_29_11
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