Nuprl Lemma : ma-ring-diff
R:Id List. s:{i:Id| (i 
R)} 
{i:Id| (i R)} . x:Id.
(ma-ring(R;s) 
(x R) (n:{1..||remove-repeats(IdDeq;R)||
}. (
(x = (s^n x)))))
Proof not projected
Definitions occuring in Statement :
ma-ring: ma-ring(R;s),
id-deq: IdDeq,
Id: Id,
length: ||as||,
int_seg: {i..j},
all: x:A. B[x],
not: A,
implies: P Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A B[x],
list: type List,
natural_number: $n,
equal: s = t,
l_member: (x l),
fun_exp: f^n,
remove-repeats: remove-repeats(eq;L)
Lemmas :
subtype_rel_wf,
rev_implies_wf,
squash_wf,
true_wf,
select_listify_id,
assert_wf,
iff_wf,
deq_wf,
bool_wf,
top_wf,
length_wf_nat,
int_seg_properties,
listify_length,
member_null,
pos_length2,
listify_wf,
fun_exp_wf,
int_seg_wf,
length_wf,
remove-repeats_wf,
id-deq_wf,
ma-ring_wf,
l_member_wf,
Id_wf,
ma-ring-no-repeats-listify,
le_wf,
not_wf,
false_wf,
member_wf,
nat_wf
\mforall{}R:Id List. \mforall{}s:\{i:Id| (i \mmember{} R)\} {}\mrightarrow{} \{i:Id| (i \mmember{} R)\} . \mforall{}x:Id.
(ma-ring(R;s) {}\mRightarrow{} (x \mmember{} R) {}\mRightarrow{} (\mforall{}n:\{1..||remove-repeats(IdDeq;R)||\msupminus{}\}. (\mneg{}(x = (s\^{}n x)))))
Date html generated:
2012_02_20-PM-05_58_09
Last ObjectModification:
2012_02_02-PM-02_30_10
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