{ 
[n,m:
].
nat-to-incomparable(n) 
nat-to-incomparable(m) supposing (n = m) }
{ Proof }
Definitions occuring in Statement :
nat-to-incomparable: nat-to-incomparable(n),
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
not: A,
int: 
,
atom: Atom,
equal: s = t,
iseg: l1 l2
Definitions :
tl: tl(l),
hd: hd(l),
exists: 
x:A. B[x],
nil: [],
token: "$token",
cons: [car / cdr],
nat-to-str: nat-to-str(n),
append: as @ bs,
union: left + right,
or: P 
Q,
iff: P 
Q,
real: 
,
grp_car: |g|,
subtype: S 
T,
limited-type: LimitedType,
universe: Type,
list: type List,
name: Name,
strong-subtype: strong-subtype(A;B),
ge: i 
j ,
assert: 
b,
less_than: a < b,
product: x:A 
B[x],
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
all: x:A. B[x],
le: A B,
set: {x:A| B[x]} ,
nat-to-incomparable: nat-to-incomparable(n),
equal: s = t,
int: ,
prop: 
,
lambda: 
x.A[x],
atom: Atom,
iseg: l1 l2,
uall: [x:A]. B[x],
nat: ,
not: A,
implies: P Q,
function: x:A 
B[x],
false: False,
void: Void,
uimplies: b supposing a,
isect: 
x:A. B[x],
member: t 
T,
Auto: Error :Auto,
D: Error :D,
THENM: Error :THENM,
CollapseTHEN: Error :CollapseTHEN,
Unfold: Error :Unfold,
Try: Error :Try,
THEN: Error :THEN,
CollapseTHENA: Error :CollapseTHENA,
l_member: (x l),
guard: {T},
int_seg: {i..j
},
quotient: x,y:A//B[x; y],
divides: b | a,
assoced: a ~ b,
set_car: |p|,
set_leq: a b,
set_lt: a <p b,
grp_lt: a < b,
rng_car: |r|,
unit: Unit,
nat_plus: 
,
rationals: 
,
atom: Atom$n,
dstype: dstype(TypeNames; d; a),
fset: FSet{T},
l_contains: A B,
inject: Inj(A;B;f),
reducible: reducible(a),
prime: prime(a),
squash: 
T,
l_disjoint: l_disjoint(T;l1;l2),
l_exists: (xL. P[x]),
l_all: (xL.P[x]),
apply: f a,
infix_ap: x f y,
fun-connected: y is f*(x),
qle: r s,
qless: r < s,
q-rel: q-rel(r;x),
i-finite: i-finite(I),
i-closed: i-closed(I),
p-outcome: Outcome,
fset-member: a s,
f-subset: xs ys,
fset-closed: (s closed under fs),
decidable: Dec(P),
rev_implies: P Q,
map: map(f;as),
last: last(L),
remove-repeats: remove-repeats(eq;L),
select: l[i],
bool: 
,
cand: A c B,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
eqof: eqof(d),
atom-deq: AtomDeq,
sqequal: s ~ t,
sq_type: SQType(T),
pair: <a, b>,
length: ||as||,
add: n + m,
natural_number: $n,
so_apply: x[s],
true: True,
str-to-nat: str-to-nat(s)
Lemmas :
str-to-nat-to-str,
int_subtype_base,
str-to-nat_wf,
squash_wf,
true_wf,
tl_wf,
length_wf1,
ge_wf,
hd_wf,
general-append-cancellation,
iseg_nil,
cons_iseg,
list_subtype_base,
atom_subtype_base,
length_wf_nat,
assert_wf,
subtype_base_sq,
assert-deq-member,
atom-deq_wf,
member-nat-to-str,
l_member_subtype,
member_append,
decidable__l_member,
decidable__atom_equal,
cons_member,
l_member_wf,
iseg_member,
subtype_rel_wf,
name_wf,
nat-to-incomparable_wf,
member_wf,
iseg_wf,
false_wf,
not_wf,
nat_wf,
iseg_append_iff,
append_wf,
nat-to-str_wf
\mforall{}[n,m:\mBbbN{}]. \mneg{}nat-to-incomparable(n) \mleq{} nat-to-incomparable(m) supposing \mneg{}(n = m)
Date html generated:
2011_08_10-AM-07_43_03
Last ObjectModification:
2011_06_18-AM-08_09_49
Home
Index