Nuprl Lemma : gammaFIM_fun_id
g,h:
List 
.
(spr(g)
(a: List. (((g a) = 0) ((g (a @ [h a])) = 0)))
((g []) = 0)
(f: . ((f 
spr(g)) (f = (
n.gammaFIM(mklist(n + 1;f);g;h)[n])))))
Proof
Definitions occuring in Statement :
gammaFIM: gammaFIM(a;g;h),
in_spr: (f spr(g)),
select: l[i],
append: as @ bs,
nat: ,
all: x:A. B[x],
implies: P Q,
apply: f a,
lambda: x.A[x],
function: x:A B[x],
add: n + m,
natural_number: $n,
equal: s = t,
mklist: mklist(n;f)
Definitions :
all: x:A. B[x],
nat: ,
implies: P Q,
member: t T,
prop: 
,
le: A 
B,
not: 
A,
false: False,
so_lambda: 
x.t[x],
int_seg: {i..j
},
squash: 
T,
true: True,
lelt: i j < k,
and: P 
Q,
cand: A c B,
rev_implies: P 
Q,
iff: P Q,
uall: [x:A]. B[x],
so_apply: x[s],
uimplies: b supposing a,
in_spr: (f spr(g)),
guard: {T}
Lemmas :
in_spr_wf,
nat_wf,
equal_wf,
Error :nil_wf,
le_wf,
all_wf,
Error :list_wf,
append_wf,
Error :cons_wf,
spr_wf,
select_wf,
gammaFIM_wf,
mklist_wf,
subtype_rel_dep_function,
int_seg_wf,
subtype_rel_sets,
lelt_wf,
squash_wf,
length_wf,
gammaFIM_id,
gammaFIM_equi_length_mklist,
mklist_select
\mforall{}g,h:\mBbbN{} List {}\mrightarrow{} \mBbbN{}.
(spr(g)
{}\mRightarrow{} (\mforall{}a:\mBbbN{} List. (((g a) = 0) {}\mRightarrow{} ((g (a @ [h a])) = 0)))
{}\mRightarrow{} ((g []) = 0)
{}\mRightarrow{} (\mforall{}f:\mBbbN{} {}\mrightarrow{} \mBbbN{}. ((f \mmember{} spr(g)) {}\mRightarrow{} (f = (\mlambda{}n.gammaFIM(mklist(n + 1;f);g;h)[n])))))
Date html generated:
2013_03_20-AM-10_33_48
Last ObjectModification:
2013_03_16-PM-07_58_15
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