Nuprl Lemma : ma-ring-remove-repeats-eq-set-listify
R:Id List. s:{i:Id| (i 
R)} 
{i:Id| (i R)} . x:Id.
(ma-ring(R;s) 
(x R) l_eqset(Id;remove-repeats(IdDeq;R);(
n.(s^n x))[
||remove-repeats(IdDeq;R)||]))
Proof not projected
Definitions occuring in Statement :
ma-ring: ma-ring(R;s),
l_eqset: l_eqset(T;L1;L2),
id-deq: IdDeq,
Id: Id,
listify: listify(f;m;n),
length: ||as||,
all: x:A. B[x],
implies: P Q,
set: {x:A| B[x]} ,
apply: f a,
lambda: x.A[x],
function: x:A B[x],
list: type List,
natural_number: $n,
l_member: (x l),
fun_exp: f^n,
remove-repeats: remove-repeats(eq;L)
Lemmas :
decidable__equal_Id,
decidable__l_member,
sq_stable_from_decidable,
atom2_subtype_base,
false_wf,
not_wf,
nat_properties,
subtype_base_sq,
int_subtype_base,
int_seg_properties,
rev_implies_wf,
select_listify_id,
assert_wf,
bool_wf,
length_wf_nat,
top_wf,
deq_wf,
non_neg_length,
listify_length,
select_wf,
member_wf,
subtype_rel_wf,
member-remove-repeats,
ma-ring-all-in-remove-repeats-steps1,
inject_wf,
int_seg_wf,
l_member_wf,
Id_wf,
le_wf,
fun_exp_wf,
length_wf,
remove-repeats_wf,
listify_wf,
nat_wf,
id-deq_wf,
iff_wf,
ma-ring_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{} l\_eqset(Id;remove-repeats(IdDeq;R);(\mlambda{}n.(s\^{}n x))[\mBbbN{}||remove-repeats(IdDeq;R)||]))
Date html generated:
2012_02_20-PM-05_56_07
Last ObjectModification:
2012_02_02-PM-02_29_53
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