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;

theorem Th11:
  for p being PartState of S, d being data-only PartState of S
  holds IC(p+*d) = IC p
proof
  let p be PartState of S, d be data-only PartState of S;
A1: not IC S in dom d by Th10;
  thus IC(p+*d) = IC p by A1,FUNCT_4:11;
end;
