{ 
[T:Type]. [eq:EqDecider(T)]. [L:T List].
Inj({x:T| (x 
L)} ;
||L||;
x.index(L;x)) supposing no_repeats(T;L) }
{ Proof }
Definitions occuring in Statement :
l_index: index(L;x),
length: ||as||,
inject: Inj(A;B;f),
int_seg: {i..j
},
uimplies: b supposing a,
uall: [x:A]. B[x],
set: {x:A| B[x]} ,
lambda: x.A[x],
list: type List,
natural_number: $n,
universe: Type,
no_repeats: no_repeats(T;l),
l_member: (x l),
deq: EqDecider(T)
Definitions :
cand: A c
B,
exists: 
x:A. B[x],
nat: ,
lelt: i 
j < k,
real: 
,
rationals: 
,
subtype: S 
T,
int: 
,
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
less_than: a < b,
product: x:A 
B[x],
and: P Q,
uiff: uiff(P;Q),
void: Void,
false: False,
not: 
A,
assert: 
b,
subtype_rel: A r B,
l_index: index(L;x),
apply: f a,
length: ||as||,
natural_number: $n,
axiom: Ax,
int_seg: {i..j},
l_member: (x l),
set: {x:A| B[x]} ,
lambda: x.A[x],
implies: P 
Q,
inject: Inj(A;B;f),
uimplies: b supposing a,
prop: 
,
list: type List,
deq: EqDecider(T),
universe: Type,
no_repeats: no_repeats(T;l),
uall: [x:A]. B[x],
isect: 
x:A. B[x],
member: t T,
equal: s = t,
all: x:A. B[x],
function: x:A 
B[x],
Auto: Error :Auto,
Complete: Error :Complete,
Try: Error :Try,
CollapseTHEN: Error :CollapseTHEN,
tactic: Error :tactic,
limited-type: LimitedType,
pair: <a, b>,
true: True,
squash: 
T,
D: Error :D,
CollapseTHENA: Error :CollapseTHENA,
RepeatFor: Error :RepeatFor,
grp_car: |g|,
bool: 
,
sq_type: SQType(T),
select: l[i],
guard: {T},
sqequal: s ~ t,
so_lambda: 
x.t[x],
MaAuto: Error :MaAuto
Lemmas :
set_subtype_base,
int_subtype_base,
squash_wf,
subtype_rel_wf,
no_repeats_l_index,
int_seg_properties,
nat_properties,
select_member,
length_wf_nat,
subtype_base_sq,
select_wf,
le_wf,
false_wf,
not_wf,
member_wf,
nat_wf,
l_index_wf,
l_member_wf,
length_wf1,
int_seg_wf,
inject_wf,
no_repeats_wf,
deq_wf
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[L:T List].
Inj(\{x:T| (x \mmember{} L)\} ;\mBbbN{}||L||;\mlambda{}x.index(L;x)) supposing no\_repeats(T;L)
Date html generated:
2011_08_10-AM-07_52_40
Last ObjectModification:
2011_06_18-AM-08_14_42
Home
Index