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
 for S being IC-Ins-separated non empty
 with_non-empty_values Mem-Struct over N
 for p,q being PartState of S
 holds Initialize p c= q implies Start-At(0,S) c= q
proof
 let S be IC-Ins-separated non empty
 with_non-empty_values Mem-Struct over N;
 let p,q be PartState of S;
  Start-At(0,S) c= Initialize p by FUNCT_4:25;
 hence thesis by XBOOLE_1:1;
end;
