theorem Th64:
 for k being Nat holds IC S in dom DecIC(p,k)
proof let k be Nat;
A1: dom DecIC(p,k) = dom p \/ dom Start-At(IC p-'k,S) by FUNCT_4:def 1;
  IC S in dom Start-At(IC p-'k,S) by Th15;
  hence thesis by A1,XBOOLE_0:def 3;
end;
