reserve x,N for set,
        k for Nat;
reserve N for with_zero set;
reserve S for IC-Ins-separated non empty with_non-empty_values
     Mem-Struct over N;
reserve s for State of S;
reserve p for PartState of S;

theorem Th18:
  for s being State of S holds Start-At(IC s,S) = s | {IC S}
proof
  let s be State of S;
A1: IC S in dom s by Th2;
  thus Start-At(IC s,S) = {[IC S,s.IC S]} by FUNCT_4:82
    .= s | {IC S} by A1,GRFUNC_1:28;
end;
