
theorem
  for x1,x2,x3,x4,x5,x6,x7,x8,x9,x10 being set, p being FinSequence st p
  =<*x1*>^<*x2*>^<*x3*>^<*x4*>^<*x5*>^<*x6*>^<*x7*>^<*x8*>^<*x9*>^<*x10*> holds
len p = 10 & p.1 = x1 & p.2 = x2 & p.3 = x3 & p.4 = x4 & p.5 = x5 & p.6 = x6 &
  p.7 = x7 & p.8 = x8 & p.9 = x9 & p.10 = x10
proof
  let x1,x2,x3,x4,x5,x6,x7,x8,x9,x10 be set, p be FinSequence;
  set pa = <*x1*>^<*x2*>^<*x3*>^<*x4*>^<*x5*>^<*x6*>^<*x7*>^<*x8*>^<*x9*>;
A1: pa.1 = x1 & pa.2 = x2 by FINSEQ_1:71;
A2: pa.5 = x5 & pa.6 = x6 by FINSEQ_1:71;
A3: pa.7 = x7 & pa.8 = x8 by FINSEQ_1:71;
A4: len pa = 9 by FINSEQ_1:71;
  then
A5: dom pa = Seg 9 by FINSEQ_1:def 3;
  then
A6: 3 in dom pa & 4 in dom pa by FINSEQ_1:1;
A7: pa.9 = x9 & 9 in dom pa by A5,FINSEQ_1:1,71;
  assume
A8: p = <*x1*>^<*x2*>^<*x3*>^<*x4*>^<*x5*>^<*x6*>^<*x7*>^<*x8*>^<*x9*>^
  <*x10*>;
  hence len p = len pa + len <*x10*> by FINSEQ_1:22
    .= 9 + 1 by A4,FINSEQ_1:40
    .= 10;
A9: pa.3 = x3 & pa.4 = x4 by FINSEQ_1:71;
A10: 7 in dom pa & 8 in dom pa by A5,FINSEQ_1:1;
A11: 5 in dom pa & 6 in dom pa by A5,FINSEQ_1:1;
  1 in dom pa & 2 in dom pa by A5,FINSEQ_1:1;
  hence
  p.1 = x1 & p.2 = x2 & p.3 = x3 & p.4 = x4 & p.5 = x5 & p.6 = x6 & p.7 =
  x7 & p.8 = x8 & p.9 = x9 by A8,A1,A9,A2,A3,A6,A11,A10,A7,FINSEQ_1:def 7;
  thus p.10 = p.(len pa + 1) by A4
    .= x10 by A8,FINSEQ_1:42;
end;
