theorem
  for s1,s2 being State of SCM+FSA st IC s1 = IC s2 &
  (for a being Int-Location holds s1.a = s2.a) &
  (for f being FinSeq-Location holds s1.f = s2.f)
    holds s1 = s2
proof
  let s1,s2 be State of SCM+FSA such that
A1: IC s1 = IC s2;
    IC SCM+FSA in dom s1 & IC SCM+FSA in dom s2 by MEMSTR_0:2;
    then
A2:  s1 = DataPart s1 +* Start-At (IC s1,SCM+FSA) &
     s2 = DataPart s2 +* Start-At (IC s2,SCM+FSA) by MEMSTR_0:26;
  assume that
A3: for a being Int-Location holds s1.a = s2.a and
A4: for f being FinSeq-Location holds s1.f = s2.f;
   DataPart s1 = DataPart s2
    proof
A5:   dom DataPart s1 = Data-Locations SCM+FSA by MEMSTR_0:9;
     hence dom DataPart s1 = dom DataPart s2 by MEMSTR_0:9;
     let x be object;
     assume
A6:     x in dom DataPart s1;
      then
A7:    x in Int-Locations \/ FinSeq-Locations by A5,Th92;
     per cases by A7,XBOOLE_0:def 3;
     suppose x in Int-Locations;
      then
A8:   x is Int-Location by AMI_2:def 16;
     thus (DataPart s1).x = s1.x by A6,A5,FUNCT_1:49
         .= s2.x by A8,A3
         .= (DataPart s2).x by A6,A5,FUNCT_1:49;
     end;
     suppose x in FinSeq-Locations;
      then
A9:   x is FinSeq-Location by Def3;
     thus (DataPart s1).x = s1.x by A6,A5,FUNCT_1:49
         .= s2.x by A9,A4
         .= (DataPart s2).x by A6,A5,FUNCT_1:49;
     end;
    end;
  hence thesis by A1,A2;
end;
