Nuprl Lemma : list-in-fin_spr_unfold
B:
List 
. a: List.
((a 
fspr(B)) ~ if (||a|| =
0) then tt else (firstn(||a|| - 1;a) fspr(B)) 
last(a) 
z B firstn(||a|| - 1;a) fi )
Proof
Definitions occuring in Statement :
list-in-fin_spr: (a fspr(B)),
firstn: firstn(n;as),
length: ||as||,
eq_int: (i = j),
le_int: i z j,
band: p q,
ifthenelse: if b then t else f fi ,
btrue: tt,
nat: ,
all: x:A. B[x],
apply: f a,
function: x:A B[x],
subtract: n - m,
natural_number: $n,
sqequal: s ~ t,
last: last(L)
Definitions :
all: x:A. B[x],
member: t T,
exists: 
x:A. B[x],
nat: ,
ifthenelse: if b then t else f fi ,
btrue: tt,
band: p q,
list-in-fin_spr: (a fspr(B)),
implies: P 
Q,
bfalse: ff,
so_lambda: 
x.t[x],
sq_type: SQType(T),
uall: [x:A]. B[x],
uimplies: b supposing a,
guard: {T},
bool: 
,
unit: Unit,
uiff: uiff(P;Q),
and: P Q,
so_apply: x[s],
assert: 
b,
bnot: 
b,
or: P 
Q,
true: True,
false: False,
it: 
,
prop: 
Lemmas :
subtype_base_sq,
bool_wf,
bool_subtype_base,
base_sq,
Error :list_wf,
nat_wf,
Error :list_ind_reverse_unfold1,
btrue_wf,
eqtt_to_assert,
le_int_wf,
subtype_rel_set_simple,
le_wf,
eq_int_wf,
length_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
Error :assert-bnot,
neg_assert_of_eq_int,
list-in-fin_spr_wf,
firstn_wf,
last_wf,
subtype_rel_list,
Error :non_null_iff_length,
top_wf,
subtype_top,
non_neg_length,
length_wf_nat
\mforall{}B:\mBbbN{} List {}\mrightarrow{} \mBbbN{}. \mforall{}a:\mBbbN{} List.
((a \mmember{} fspr(B)) \msim{} if (||a|| =\msubz{} 0)
then tt
else (firstn(||a|| - 1;a) \mmember{} fspr(B)) \mwedge{}\msubb{} last(a) \mleq{}z B firstn(||a|| - 1;a)
fi )
Date html generated:
2013_03_20-AM-10_35_07
Last ObjectModification:
2013_03_11-PM-00_46_39
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