reserve A for QC-alphabet;
reserve k,n,m for Nat;
reserve P for QC-pred_symbol of A;
reserve F for Element of QC-WFF(A);
reserve Q for QC-pred_symbol of A;
reserve F, G for (Element of QC-WFF(A)), s for FinSequence;
reserve p for Element of QC-WFF(A);

theorem Th15:
  p is conjunctive implies len @the_left_argument_of p < len @p &
  len @the_right_argument_of p < len @p
proof
  assume
A1: p is conjunctive;
  then consider l, q being Element of QC-WFF(A) such that
A2: p = l '&' q;
  p = <*[2, 0]*>^(@l^@q) by A2,FINSEQ_1:32;
  then
A3: len @p = len <*[2, 0]*> + len (@l^@q) by FINSEQ_1:22
    .= len (@l^@q) + 1 by FINSEQ_1:40;
A4: len @q + len @l = len (@l^@q) by FINSEQ_1:22;
  then len @q <= len (@l^@q) by NAT_1:11;
  then
A5: len @q < len @p by A3,NAT_1:13;
  len @l <= len (@l^@q) by A4,NAT_1:11;
  then len @l < len @p by A3,NAT_1:13;
  hence thesis by A1,A2,A5,Def25,Def26;
end;
