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 Th36:
 for p being PartState of S, k,l being Nat
  holds p +* Start-At(k,S) +* Start-At(l,S)  = p +* Start-At(l,S)
proof let p be PartState of S, k,l be Nat;
  dom Start-At(k,S) = {IC S}
    .= dom Start-At(l,S);
 hence p +* Start-At(k,S) +* Start-At(l,S)  = p +* Start-At(l,S) by FUNCT_4:74;
end;
