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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