reserve j, k, m for Nat;

theorem Th2:
  for k,loc being Nat, a being Data-Location
   holds IncAddr(a=0_goto loc,k) = a=0_goto (loc + k)
proof
  let k,loc be Nat, a be Data-Location;
A1: InsCode IncAddr(a=0_goto loc,k) = InsCode(a=0_goto loc) by COMPOS_0:def 9
     .= 7
     .= InsCode(a=0_goto(loc + k));
A2: AddressPart IncAddr(a=0_goto loc,k) = AddressPart(a=0_goto loc)
           by COMPOS_0:def 9
     .= <*a*>
     .= AddressPart(a=0_goto (loc + k));
A3: JumpPart IncAddr(a=0_goto loc,k) = k + JumpPart(a=0_goto loc)
                   by COMPOS_0:def 9;
  JumpPart IncAddr(a=0_goto loc,k) = JumpPart(a=0_goto (loc + k))
   proof
    thus
A4:   dom JumpPart IncAddr(a=0_goto loc,k)
     = dom JumpPart(a=0_goto (loc + k)) by A1,COMPOS_0:def 5;
    let x be object;
    assume
A5:   x in dom JumpPart IncAddr(a=0_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(a=0_goto loc,k)).x
      = k + (JumpPart(a=0_goto loc)).x by A3,A5,VALUED_1:def 2
     .= loc + k by A6
     .= (JumpPart(a=0_goto(loc + k))).x by A6;
   end;
 hence thesis by A1,A2,COMPOS_0:1;
end;
