Nuprl Lemma : rotate-ring-property1
T:Type. L1,L2:T List. (rotate-ring(T;L1;L2) 
(x:T. ((x 
L1) 
(x L2))))
Proof not projected
Definitions occuring in Statement :
rotate-ring: rotate-ring(T;L1;L2),
all: x:A. B[x],
iff: P Q,
implies: P Q,
list: type List,
universe: Type,
l_member: (x l)
Definitions :
function: x:A 
B[x],
all: x:A. B[x],
isect: 
x:A. B[x],
uall: [x:A]. B[x],
equal: s = t,
member: t T,
rotate-ring: rotate-ring(T;L1;L2),
universe: Type,
list: type List,
product: x:A 
B[x],
and: P 
Q,
iff: P Q,
prop: 
,
implies: P Q,
exists: 
x:A. B[x],
int_seg: {i..j
},
l_member: (x l),
rev_implies: P Q,
int: 
,
length: ||as||,
nat: 
,
cand: A c B,
less_than: a < b,
CollapseTHEN: Error :CollapseTHEN,
ifthenelse: if b then t else f fi ,
le_int: i 
z j,
add: n + m,
subtract: n - m,
MaAuto: Error :MaAuto,
CollapseTHENA: Error :CollapseTHENA,
Auto: Error :Auto,
bool: 
,
select: l[i],
natural_number: $n,
lt_int: i <z j,
set: {x:A| B[x]} ,
pair: <a, b>,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
lelt: i j < k,
ge: i 
j ,
le: A B,
subtype: S 
T,
rationals: 
,
real: 
,
not: 
A,
false: False,
void: Void,
minus: -n,
subtype_rel: A r B,
uiff: uiff(P;Q),
uimplies: b supposing a,
strong-subtype: strong-subtype(A;B),
sq_type: SQType(T),
guard: {T},
union: left + right,
unit: Unit,
bnot: 
b,
assert: 
b,
bor: p 
q,
band: p q,
bimplies: p q,
es-ble: e loc e',
es-bless: e <loc e',
es-eq-E: e = e',
eq_lnk: a = b,
eq_id: a = b,
name_eq: name_eq(x;y),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-member: deq-member(eq;x;L),
q_le: q_le(r;s),
q_less: q_less(r;s),
qeq: qeq(r;s),
eq_atom: eq_atom$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),
btrue: tt,
bfalse: ff,
limited-type: LimitedType,
or: P Q,
so_apply: x[s],
grp_car: |g|,
fpf: a:A fp-> B[a],
eclass: EClass(A[eo; e]),
sqequal: s ~ t
Lemmas :
int_subtype_base,
bnot_of_lt_int,
bool_subtype_base,
subtype_base_sq,
bool_cases,
select_wf,
bnot_wf,
ifthenelse_wf,
le_int_wf,
int_seg_wf,
nat_wf,
member_wf,
not_wf,
false_wf,
length_wf_nat,
eqtt_to_assert,
assert_of_le_int,
le_wf,
uiff_transitivity,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int,
lt_int_wf,
nat_properties,
int_seg_properties,
bool_wf,
assert_wf,
l_member_wf,
rev_implies_wf,
iff_wf,
rotate-ring_wf
\mforall{}T:Type. \mforall{}L1,L2:T List. (rotate-ring(T;L1;L2) {}\mRightarrow{} (\mforall{}x:T. ((x \mmember{} L1) \mLeftarrow{}{}\mRightarrow{} (x \mmember{} L2))))
Date html generated:
2012_02_20-PM-05_54_21
Last ObjectModification:
2012_02_02-PM-02_29_09
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