Nuprl Lemma : ma-ring-diff-circle
[R:Id List]. [s:{i:Id| (i 
R)} 
{i:Id| (i R)} ]. [x:Id].
(ma-ring(R;s) 
(x R) (y:{i:Id| (i R)} . ((
(x = y)) ((y = (s^||remove-repeats(IdDeq;R)|| x))))))
Proof not projected
Definitions occuring in Statement :
ma-ring: ma-ring(R;s),
id-deq: IdDeq,
Id: Id,
length: ||as||,
uall: [x:A]. B[x],
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,
equal: s = t,
l_member: (x l),
fun_exp: f^n,
remove-repeats: remove-repeats(eq;L)
Lemmas :
squash_wf,
true_wf,
ma-ring-diff,
sq_stable_from_decidable,
decidable__l_member,
decidable__equal_Id,
set_subtype_base,
atom2_subtype_base,
fun_exp_add-sq,
int_subtype_base,
subtype_base_sq,
int_seg_properties,
ma-ring-all-in-remove-repeats-steps2,
subtype_rel_list,
strong-subtype_wf,
strong-subtype-deq-subtype,
non_neg_length,
length_wf,
le_wf,
nat_wf,
intensional-universe_wf,
subtype_rel_wf,
ma-ring_wf,
not_wf,
false_wf,
fun_exp_wf,
l_member_wf,
length_wf_nat,
remove-repeats_wf,
assert_wf,
iff_wf,
id-deq_wf,
Id_wf,
deq_wf,
member_wf,
bool_wf,
top_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{}y:\{i:Id| (i \mmember{} R)\} . ((\mneg{}(x = y)) {}\mRightarrow{} (\mneg{}(y = (s\^{}||remove-repeats(IdDeq;R)|| x))))))
Date html generated:
2012_02_20-PM-05_58_15
Last ObjectModification:
2012_02_02-PM-02_30_13
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