reserve k for Nat;

theorem Th4:
  for N be with_zero set
  for S be relocable halting IC-Ins-separated
  non empty with_non-empty_values AMI-Struct over N
  for INS being Instruction of S, s being State of S
   holds  Exec(IncAddr(INS,k),IncIC(s,k)) =  IncIC(Exec(INS,s),k)
 proof
  let N be with_zero set;
  let S be relocable halting IC-Ins-separated
  non empty with_non-empty_values AMI-Struct over N;
  let INS be Instruction of S, s be State of S;
  thus  Exec(IncAddr(INS,k),IncIC(s,k))
          =  Exec(IncAddr(INS,(0 qua Nat)+k),IncIC(s,k))
         .=  IncIC(Exec(IncAddr(INS,0),s),k) by Def1
         .=  IncIC(Exec(INS,s),k) by COMPOS_0:3;
 end;
