Nuprl Lemma : fin_spr_mem_in_fin_spr
delete the set type fin_spr as it hides the set prop
use in_fin_spr instead.
till that happens, this and the next lemma will help
with interconversion
B:
List 
. f:fin_spr(B). (f 
fspr(B))
Proof
Definitions occuring in Statement :
in_fin_spr: (f fspr(B)),
fin_spr: fin_spr(B),
nat: ,
all: x:A. B[x],
function: x:A B[x]
Definitions :
all: x:A. B[x],
member: t T,
nat: ,
in_fin_spr: (f fspr(B)),
int_seg: {i..j
},
so_lambda: 
x.t[x],
lelt: i 
j < k,
implies: P 
Q,
and: P 
Q,
le: A B,
sq_stable: SqStable(P),
squash: 
T,
not: 
A,
false: False,
true: True,
uall: [x:A]. B[x],
fin_spr: fin_spr(B),
prop: 
,
uimplies: b supposing a,
so_apply: x[s]
Lemmas :
fin_spr_wf,
Error :list_wf,
nat_wf,
le_wf,
mklist_wf,
subtype_rel_dep_function,
int_seg_wf,
subtype_rel_sets,
lelt_wf,
squash_wf,
sq_stable__all,
Error :sq_stable__le
\mforall{}B:\mBbbN{} List {}\mrightarrow{} \mBbbN{}. \mforall{}f:fin\_spr(B). (f \mmember{} fspr(B))
Date html generated:
2013_03_20-AM-10_34_35
Last ObjectModification:
2013_03_17-PM-04_22_47
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