Nuprl Lemma : ma-ring-id

R:Id List. s:{i:Id| (i  R)}   {i:Id| (i  R)} . x:Id. n:.
  (ma-ring(R;s)  (x  R)  (x = (s^n x))  (k:. (n = (k * ||remove-repeats(IdDeq;R)||))))


Proof not projected




Definitions occuring in Statement :  ma-ring: ma-ring(R;s) id-deq: IdDeq Id: Id length: ||as|| nat: all: x:A. B[x] exists: x:A. B[x] implies: P  Q set: {x:A| B[x]}  apply: f a function: x:A  B[x] list: type List multiply: n * m equal: s = t l_member: (x  l) fun_exp: f^n remove-repeats: remove-repeats(eq;L)
Definitions :  prop: member: t  T implies: P  Q all: x:A. B[x] gt: i > j or: P  Q true: True squash: T nat_plus: uall: [x:A]. B[x] false: False not: A le: A  B nat: uimplies: b supposing a
Lemmas :  nat_wf ma-ring_wf l_member_wf fun_exp_wf Id_wf equal_wf ma-ring-remove-repeats-id length_wf_nat id-deq_wf remove-repeats_wf length_wf fun_exp-rem

\mforall{}R:Id  List.  \mforall{}s:\{i:Id|  (i  \mmember{}  R)\}    {}\mrightarrow{}  \{i:Id|  (i  \mmember{}  R)\}  .  \mforall{}x:Id.  \mforall{}n:\mBbbN{}.
    (ma-ring(R;s)  {}\mRightarrow{}  (x  \mmember{}  R)  {}\mRightarrow{}  (x  =  (s\^{}n  x))  {}\mRightarrow{}  (\mexists{}k:\mBbbN{}.  (n  =  (k  *  ||remove-repeats(IdDeq;R)||))))


Date html generated: 2012_02_20-PM-05_58_27
Last ObjectModification: 2012_02_02-PM-02_30_20

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