
theorem
  for D being non empty set,k1,k2 being Nat holds
  mid(<*>D,k1,k2)=<*>D
proof
  let D be non empty set,k1,k2 be Nat;
  per cases;
  suppose k1<=k2;
    hence mid(<*>D,k1,k2)=((<*>D)/^(k1-'1))|(k2-'k1+1) by FINSEQ_6:def 3
      .= (<*>D)|(k2-'k1+1) by FINSEQ_6:80
      .=<*>D by FINSEQ_5:78;
  end;
  suppose k1>k2;
    hence mid(<*>D,k1,k2)=Rev (((<*>D)/^(k2-'1))|(k1-'k2+1)) by FINSEQ_6:def 3
      .= Rev((<*>D)|(k1-'k2+1)) by FINSEQ_6:80
      .= Rev(<*>D) by FINSEQ_5:78
      .=<*>D by FINSEQ_5:79;
  end;
end;
