reserve x,y,z for set;
reserve f,f1,f2,f3 for FinSequence,
  p,p1,p2,p3 for set,
  i,k for Nat;
reserve D for non empty set,
  p,p1,p2,p3 for Element of D,
  f,f1,f2 for FinSequence of D;

theorem Th86:
  f just_once_values p implies Rev(f|--p) = Rev f -|p
proof
  assume
A1: f just_once_values p;
  then
A2: p in rng f by FINSEQ_4:5;
  then
A3: p in rng Rev f by FINSEQ_5:57;
  then reconsider n = p..Rev f - 1 as Element of NAT
             by FINSEQ_4:21,INT_1:5;
  p..f + p..Rev f = len f + 1 by A1,Th37;
  then
A4: n + p..f = len f;
  Rev(f|--p) = Rev(f/^(p..f)) by A2,FINSEQ_5:35
    .= (Rev f) | n by A4,Th84
    .= (Rev f) | Seg n;
  hence thesis by A3,FINSEQ_4:def 5;
end;
