{ 
n:
. s:Atom. ((s 
nat-to-str(n)) 
(s ``0 1 2 3 4 5 6 7 8 9``)) }
{ Proof }
Definitions occuring in Statement :
nat-to-str: nat-to-str(n),
nat: ,
all: x:A. B[x],
implies: P Q,
cons: [car / cdr],
nil: [],
token: "$token",
atom: Atom,
l_member: (x l)
Definitions :
nat: ,
sqequal: s ~ t,
function: x:A 
B[x],
all: x:A. B[x],
not: 
A,
atom: Atom,
equal: s = t,
l_member: (x l),
natural_number: $n,
member: t T,
token: "$token",
int: 
,
less_than: a < b,
universe: Type,
le: A 
B,
prop: 
,
product: x:A 
B[x],
and: P 
Q,
lelt: i j < k,
implies: P Q,
false: False,
void: Void,
set: {x:A| B[x]} ,
int_seg: {i..j
},
p-outcome: Outcome,
strong-subtype: strong-subtype(A;B),
subtype_rel: A 
r B,
exists: 
x:A. B[x],
guard: {T},
rationals: 
,
subtype: S T,
real: 
,
add: n + m,
pair: <a, b>,
nil: [],
cons: [car / cdr],
nat-to-str: nat-to-str(n),
bool: 
,
list: type List,
tl: tl(l),
hd: hd(l),
sq_type: SQType(T),
apply: f a,
so_apply: x[s],
union: left + right,
or: P 
Q,
append: as @ bs,
iff: P 
Q,
assert: 
b,
bfalse: ff,
eq_int: (i =
j),
limited-type: LimitedType,
bnot: 
b,
btrue: tt,
eq_atom: x =a y,
null: null(as),
set_blt: Error :set_blt,
infix_ap: x f y,
grp_blt: Error :grp_blt,
b-exists: (i<n.P[i])_b,
bl-exists: (xL.P[x])_b,
bl-all: (xL.P[x])_b,
dcdr-to-bool: [d],
eq_type: eq_type(T;T'),
eq_atom: eq_atom$n(x;y),
q_le: q_le(r;s),
q_less: q_less(a;b),
qeq: qeq(r;s),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-member: deq-member(eq;x;L),
bimplies: p q,
band: p q,
bor: p q,
lt_int: i <z j,
le_int: i z j,
rev_implies: P Q,
subtract: n - m,
grp_car: Error :grp_car,
minus: -n,
ge: i 
j ,
THENL_cons: Error :THENL_nil,
tactic: Error :tactic,
THENL_cons: Error :THENL_cons,
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
Auto: Error :Auto,
SplitOn: Error :SplitOn,
CollapseTHENA: Error :CollapseTHENA,
THENL_v2: Error :THENL,
RepeatFor: Error :RepeatFor,
proper-iseg: L1 < L2,
remainder: n rem m,
length: ||as||,
iseg: l1 l2,
gt: i > j,
nat_plus: 
,
divide: n 
m,
D: Error :D,
THENM: Error :THENM,
nequal: a 
b T ,
int_nzero: 
,
multiply: n * m
Lemmas :
rem_bounds_1,
div_rem_sum,
int_nzero_wf,
nequal_wf,
member_append,
nat_plus_wf,
divide_wf,
remainder_wf,
nat_properties,
ge_wf,
nat-to-str_wf,
cons_member,
bool_cases,
eqtt_to_assert,
bool_sq,
eqff_to_assert,
iff_transitivity,
assert_of_bnot,
not_functionality_wrt_iff,
assert_of_eq_int,
eq_int_wf,
bool_wf,
bnot_wf,
not_wf,
assert_wf,
member_singleton,
atom_sq,
l_member_wf,
select_member,
nat_wf,
member_wf,
le_wf
\mforall{}n:\mBbbN{}. \mforall{}s:Atom. ((s \mmember{} nat-to-str(n)) {}\mRightarrow{} (s \mmember{} ``0 1 2 3 4 5 6 7 8 9``))
Date html generated:
2010_08_26-PM-11_30_25
Last ObjectModification:
2010_04_23-PM-05_02_40
Home
Index