Nuprl Lemma : gammaFIM_true
g,h:
List 
.
(spr(g)
(a: List. (((g a) = 0) ((g (a @ [h a])) = 0)))
((g []) = 0)
(L: List. ((g gammaFIM(L;g;h)) = 0)))
Proof
Definitions occuring in Statement :
gammaFIM: gammaFIM(a;g;h),
append: as @ bs,
nat: ,
all: x:A. B[x],
implies: P Q,
apply: f a,
function: x:A B[x],
natural_number: $n,
equal: s = t
Definitions :
all: x:A. B[x],
nat: ,
implies: P Q,
gammaFIM: gammaFIM(a;g;h),
member: t 
T,
prop: 
,
le: A 
B,
not: 
A,
false: False,
so_lambda: 
x.t[x],
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
exists: 
x:A. B[x],
true: True,
squash: 
T,
top: Top,
uall: [x:A]. B[x],
so_apply: x[s],
bool: 
,
guard: {T},
unit: Unit,
uimplies: b supposing a,
assert: 
b,
uiff: uiff(P;Q),
and: P 
Q,
bnot: 
b,
or: P 
Q,
sq_type: SQType(T),
it: 
Lemmas :
Error :list_wf,
nat_wf,
equal_wf,
Error :nil_wf,
le_wf,
all_wf,
append_wf,
Error :cons_wf,
spr_wf,
Error :list_ind_reverse_wf_dependent,
eq_int_wf,
subtype_rel_set_simple,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
Error :assert-bnot,
neg_assert_of_eq_int,
top_wf,
Error :list_ind_reverse_wf
\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{}L:\mBbbN{} List. ((g gammaFIM(L;g;h)) = 0)))
Date html generated:
2013_03_20-AM-10_33_13
Last ObjectModification:
2013_03_08-PM-11_00_16
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