reserve j, k, m for Nat;

theorem Th1:
  for k,loc being Nat
  holds IncAddr(SCM-goto loc,k) = SCM-goto (loc + k)
proof
  let k,loc be Nat;
A1: InsCode IncAddr(SCM-goto loc,k) = InsCode SCM-goto loc by COMPOS_0:def 9
     .= 6
     .= InsCode SCM-goto (loc + k);
A2: AddressPart IncAddr(SCM-goto loc,k) = AddressPart SCM-goto loc
           by COMPOS_0:def 9
     .= {}
     .= AddressPart SCM-goto (loc + k);
A3: JumpPart IncAddr(SCM-goto loc,k) = k + JumpPart SCM-goto loc
                   by COMPOS_0:def 9;
  JumpPart IncAddr(SCM-goto loc,k) = JumpPart SCM-goto (loc + k)
   proof
    thus
A4:   dom JumpPart IncAddr(SCM-goto loc,k)
     = dom JumpPart SCM-goto (loc + k) by A1,COMPOS_0:def 5;
    let x be object;
    assume
A5:   x in dom JumpPart IncAddr(SCM-goto loc,k);
     dom <*loc+k*> = {1} by FINSEQ_1:2,38;
     then
A6:   x = 1 by A5,A4,TARSKI:def 1;
    thus (JumpPart IncAddr(SCM-goto loc,k)).x
      = k + (JumpPart SCM-goto loc).x by A3,A5,VALUED_1:def 2
     .= loc + k by A6
     .= (JumpPart SCM-goto(loc + k)).x by A6;
   end;
 hence thesis by A1,A2,COMPOS_0:1;
end;
