reserve x,y for Element of REAL;
reserve i,j,k for Element of NAT;
reserve a,b for Element of REAL;

theorem Th23:
  for x,y,z being Element of REAL holds +(x,+(y,z)) = +(+(x,y),z)
proof
  let x,y,z be Element of REAL;
A1: x in REAL+ \/ [:{0},REAL+:] & y in REAL+ \/ [:{0},REAL+:]
     by XBOOLE_0:def 5;
A2: z in REAL+ \/ [:{0},REAL+:] by XBOOLE_0:def 5;
  per cases by A1,A2,XBOOLE_0:def 3;
  suppose that
A3: x in REAL+ and
A4: y in REAL+ and
A5: z in REAL+;
A6: ex x99,y99 being Element of REAL+ st x = x99 & y = y99 & +(x,y) = x99 +
    y99 by A3,A4,Def1;
    then
A7: ex xy99,z99 being Element of REAL+ st +(x,y) = xy99 & z = z99 & +(+(x,
    y),z) = xy99 + z99 by A5,Def1;
A8: ex y9,z9 being Element of REAL+ st y = y9 & z = z9 & +( y,z) = y9 + z9
    by A4,A5,Def1;
    then
    ex x9,yz9 being Element of REAL+ st x = x9 & +(y,z) = yz9 & +(x,+(y,z))
    = x9 + yz9 by A3,Def1;
    hence thesis by A8,A6,A7,ARYTM_2:6;
  end;
  suppose that
A9: x in REAL+ and
A10: y in REAL+ and
A11: z in [:{0},REAL+:];
A12: ex x99,y99 being Element of REAL+ st x = x99 & y = y99 & +(x,y) = x99
    + y99 by A9,A10,Def1;
    then consider xy99,z99 being Element of REAL+ such that
A13: +(x,y) = xy99 and
A14: z = [0,z99] and
A15: +(+(x,y),z) = xy99 - z99 by A11,Def1;
    consider y9,z9 being Element of REAL+ such that
A16: y = y9 and
A17: z = [0,z9] and
A18: +(y,z) = y9 - z9 by A10,A11,Def1;
A19: z9 = z99 by A17,A14,XTUPLE_0:1;
    now
      per cases;
      suppose
A20:    z9 <=' y9;
        then
A21:    +(y,z) = y9 -' z9 by A18,ARYTM_1:def 2;
        then
        ex x9,yz9 being Element of REAL+ st x = x9 & +(y,z) = yz9 & +(x,+(
        y,z)) = x9 + yz9 by A9,Def1;
        hence thesis by A16,A12,A13,A15,A19,A20,A21,ARYTM_1:20;
      end;
      suppose
A22:    not z9 <=' y9;
        then
A23:    +(y,z) = [0,z9 -' y9] by A18,ARYTM_1:def 2;
        then +(y,z) in [:{0},REAL+:] by Lm1;
        then consider x9,yz9 being Element of REAL+ such that
A24:    x = x9 and
A25:    +(y,z) = [0,yz9] & +(x,+(y,z)) = x9 - yz9 by A9,Def1;
        thus +(x,+(y,z)) = x9 - (z9 -' y9) by A23,A25,XTUPLE_0:1
          .= +(+(x,y),z) by A16,A12,A13,A15,A19,A22,A24,ARYTM_1:21;
      end;
    end;
    hence thesis;
  end;
  suppose that
A26: x in REAL+ and
A27: y in [:{0},REAL+:] and
A28: z in REAL+;
    consider x99,y99 being Element of REAL+ such that
A29: x = x99 and
A30: y = [0,y99] and
A31: +(x,y) = x99 - y99 by A26,A27,Def1;
    consider z9,y9 being Element of REAL+ such that
A32: z = z9 and
A33: y = [0,y9] and
A34: +(y,z) = z9 - y9 by A27,A28,Def1;
A35: y9 = y99 by A33,A30,XTUPLE_0:1;
    now
      per cases;
      suppose that
A36:    y9 <=' x99 and
A37:    y9 <=' z9;
A38:    +(y,z) = z9 -' y9 by A34,A37,ARYTM_1:def 2;
        then consider x9,yz9 being Element of REAL+ such that
A39:    x = x9 and
A40:    +(y,z) = yz9 & +(x,+(y,z)) = x9 + yz9 by A26,Def1;
A41:    +(x,y) = x9 -' y9 by A29,A31,A35,A36,A39,ARYTM_1:def 2;
        then
        ex z99,xy99 being Element of REAL+ st z = z99 & +(x,y) = xy99 & +(
        z,+(x,y)) = z99 + xy99 by A28,Def1;
        hence thesis by A32,A29,A36,A37,A38,A39,A40,A41,ARYTM_1:12;
      end;
      suppose that
A42:    y9 <=' x99 and
A43:    not y9 <=' z9;
A44:    +(x,y) = x99 -' y9 by A31,A35,A42,ARYTM_1:def 2;
        then
A45:    ex z99,xy99 being Element of REAL+ st z = z99 & +(x,y) = xy99 & +(
        z,+(x,y)) = z99 + xy99 by A28,Def1;
A46:    +(y,z) = [0,y9 -' z9] by A34,A43,ARYTM_1:def 2;
        then +(y,z) in [:{0},REAL+:] by Lm1;
        then consider x9,yz9 being Element of REAL+ such that
A47:    x = x9 and
A48:    +(y,z) = [0,yz9] & +(x,+(y,z)) = x9 - yz9 by A26,Def1;
        thus +(x,+(y,z)) = x9 - (y9 -' z9) by A46,A48,XTUPLE_0:1
          .= +(+(x,y),z) by A32,A29,A42,A43,A47,A44,A45,ARYTM_1:22;
      end;
      suppose that
A49:    not y9 <=' x99 and
A50:    y9 <=' z9;
A51:    +(y,x) = [0,y9 -' x99] by A31,A35,A49,ARYTM_1:def 2;
        then +(y,x) in [:{0},REAL+:] by Lm1;
        then consider z99,yx99 being Element of REAL+ such that
A52:    z = z99 and
A53:    +(y,x) = [0,yx99] & +(z,+(y,x)) = z99 - yx99 by A28,Def1;
A54:    +(z,y) = z9 -' y9 by A34,A50,ARYTM_1:def 2;
        then
        ex x9,zy99 being Element of REAL+ st x = x9 & +(z,y) = zy99 & +(x,
        +(z,y)) = x9 + zy99 by A26,Def1;
        hence +(x,+(y,z)) = z99 - (y9 -' x99) by A32,A29,A49,A50,A52,A54,
ARYTM_1:22
          .= +(+(x,y),z) by A51,A53,XTUPLE_0:1;
      end;
      suppose that
A55:    not y9 <=' x99 and
A56:    not y9 <=' z9;
A57:    +(y,z) = [0,y9 -' z9] by A34,A56,ARYTM_1:def 2;
        then +(y,z) in [:{0},REAL+:] by Lm1;
        then consider x9,yz9 being Element of REAL+ such that
A58:    x = x9 and
A59:    +(y,z) = [0,yz9] & +(x,+(y,z)) = x9 - yz9 by A26,Def1;
A60:    +(y,x) = [0,y9 -' x99] by A31,A35,A55,ARYTM_1:def 2;
        then +(y,x) in [:{0},REAL+:] by Lm1;
        then consider z99,yx99 being Element of REAL+ such that
A61:    z = z99 and
A62:    +(y,x) = [0,yx99] & +(z,+(y,x)) = z99 - yx99 by A28,Def1;
        thus +(x,+(y,z)) = x9 - (y9 -' z9) by A57,A59,XTUPLE_0:1
          .= z99 - (y9 -' x99) by A32,A29,A55,A56,A61,A58,ARYTM_1:23
          .= +(+(x,y),z) by A60,A62,XTUPLE_0:1;
      end;
    end;
    hence thesis;
  end;
  suppose that
A63: x in REAL+ and
A64: y in [:{0},REAL+:] and
A65: z in [:{0},REAL+:];
    ( not(z in REAL+ & y in [:{0},REAL+:]))& not(y in REAL+ & z in [:{0},
    REAL+:]) by A64,A65,Th5,XBOOLE_0:3;
    then consider y9,z9 being Element of REAL+ such that
A66: y = [0,y9] and
A67: z = [0,z9] and
A68: +(y,z) = [0,y9 + z9] by A64,Def1;
    +(y,z) in [:{0},REAL+:] by A68,Lm1;
    then consider x9,yz9 being Element of REAL+ such that
A69: x = x9 and
A70: +(y,z) = [0,yz9] and
A71: +(x,+(y,z)) = x9 - yz9 by A63,Def1;
    consider x99,y99 being Element of REAL+ such that
A72: x = x99 and
A73: y = [0,y99] and
A74: +(x,y) = x99 - y99 by A63,A64,Def1;
A75: y9 = y99 by A66,A73,XTUPLE_0:1;
    now
      per cases;
      suppose
A76:    y99 <=' x99;
        then
A77:    +(x,y) = x99 -' y99 by A74,ARYTM_1:def 2;
        then consider xy99,z99 being Element of REAL+ such that
A78:    +(x,y) = xy99 and
A79:    z = [0,z99] and
A80:    +(+(x,y),z) = xy99 - z99 by A65,Def1;
A81:    z9 = z99 by A67,A79,XTUPLE_0:1;
        thus +(x,+(y,z)) = x9 - (y9 + z9) by A68,A70,A71,XTUPLE_0:1
          .= +(+(x,y),z) by A72,A69,A75,A76,A77,A78,A80,A81,ARYTM_1:24;
      end;
      suppose
A82:    not y99 <=' x99;
A83:    not(z in REAL+ & +(x,y) in [:{0},REAL+:]) by A65,Th5,XBOOLE_0:3;
A84:    +(x,y) = [0,y99 -' x99] by A74,A82,ARYTM_1:def 2;
        then +(x,y) in [:{0},REAL+:] by Lm1;
        then not(+(x,y) in REAL+ & z in [:{0},REAL+:]) by Th5,XBOOLE_0:3;
        then consider xy99,z99 being Element of REAL+ such that
A85:    +(x,y) = [0,xy99] and
A86:    z = [0,z99] and
A87:    +(+(x,y),z) = [0,xy99 + z99] by A84,A83,Def1,Lm1;
A88:    z9 = z99 by A67,A86,XTUPLE_0:1;
A89:    yz9 = z9 + y9 by A68,A70,XTUPLE_0:1;
        then y99 <=' yz9 by A75,ARYTM_2:19;
        then not yz9 <=' x9 by A72,A69,A82,ARYTM_1:3;
        hence +(x,+(y,z)) = [0,z9 + y9 -' x9] by A71,A89,ARYTM_1:def 2
          .= [0,z99 + (y99 -' x99)] by A72,A69,A75,A82,A88,ARYTM_1:13
          .= +(+(x,y),z) by A84,A85,A87,XTUPLE_0:1;
      end;
    end;
    hence thesis;
  end;
  suppose that
A90: z in REAL+ and
A91: y in REAL+ and
A92: x in [:{0},REAL+:];
A93: ex z99,y99 being Element of REAL+ st z = z99 & y = y99 & +(z,y) = z99
    + y99 by A90,A91,Def1;
    then consider zy99,x99 being Element of REAL+ such that
A94: +(z,y) = zy99 and
A95: x = [0,x99] and
A96: +(+(z,y),x) = zy99 - x99 by A92,Def1;
    consider y9,x9 being Element of REAL+ such that
A97: y = y9 and
A98: x = [0,x9] and
A99: +(y,x) = y9 - x9 by A91,A92,Def1;
A100: x9 = x99 by A98,A95,XTUPLE_0:1;
    now
      per cases;
      suppose
A101:   x9 <=' y9;
        then
A102:   +(y,x) = y9 -' x9 by A99,ARYTM_1:def 2;
        then ex z9,yx9 being Element of REAL+ st z = z9 & +(y,x) = yx9 & +(z,+
        (y,x)) = z9 + yx9 by A90,Def1;
        hence +(z,+(y,x)) = +(+(z,y),x) by A97,A93,A94,A96,A100,A101,A102,
ARYTM_1:20;
      end;
      suppose
A103:   not x9 <=' y9;
        then
A104:   +(y,x) = [0,x9 -' y9] by A99,ARYTM_1:def 2;
        then +(y,x) in [:{0},REAL+:] by Lm1;
        then consider z9,yx9 being Element of REAL+ such that
A105:   z = z9 and
A106:   +(y,x) = [0,yx9] & +(z,+(y,x)) = z9 - yx9 by A90,Def1;
        thus +(z,+(y,x)) = z9 - (x9 -' y9) by A104,A106,XTUPLE_0:1
          .= +(+(z,y),x) by A97,A93,A94,A96,A100,A103,A105,ARYTM_1:21;
      end;
    end;
    hence thesis;
  end;
  suppose that
A107: x in [:{0},REAL+:] and
A108: y in REAL+ and
A109: z in [:{0},REAL+:];
    consider y9,z9 being Element of REAL+ such that
A110: y = y9 and
A111: z = [0,z9] and
A112: +(y,z) = y9 - z9 by A108,A109,Def1;
    consider x99,y99 being Element of REAL+ such that
A113: x = [0,x99] and
A114: y = y99 and
A115: +(x,y) = y99 - x99 by A107,A108,Def1;
    now
      per cases;
      suppose that
A116:   x99 <=' y99 and
A117:   z9 <=' y9;
A118:   +(y,z) = y9 -' z9 by A112,A117,ARYTM_1:def 2;
        then consider x9,yz9 being Element of REAL+ such that
A119:   x = [0,x9] and
A120:   +(y,z) = yz9 & +(x,+(y,z)) = yz9 - x9 by A107,Def1;
A121:   x9 = x99 by A113,A119,XTUPLE_0:1;
        then
A122:   +(x,y) = y9 -' x9 by A110,A114,A115,A116,ARYTM_1:def 2;
        then consider z99,xy99 being Element of REAL+ such that
A123:   z = [0,z99] and
A124:   +(x,y) = xy99 & +(z,+(x,y)) = xy99 - z99 by A109,Def1;
        z9 = z99 by A111,A123,XTUPLE_0:1;
        hence thesis by A110,A114,A116,A117,A118,A120,A121,A122,A124,ARYTM_1:25
;
      end;
      suppose that
A125:   not x99 <=' y99 and
A126:   z9 <=' y9;
A127:   not(z in REAL+ & +(x,y) in [:{0},REAL+:]) by A109,Th5,XBOOLE_0:3;
A128:   +(y,x) = [0,x99 -' y99] by A115,A125,ARYTM_1:def 2;
        then +(y,x) in [:{0},REAL+:] by Lm1;
        then not(+(x,y) in REAL+ & z in [:{0},REAL+:]) by Th5,XBOOLE_0:3;
        then consider z99,yx9 being Element of REAL+ such that
A129:   z = [0,z99] and
A130:   +(y,x) = [0,yx9] & +(z,+(y,x)) = [0,z99 + yx9] by A128,A127,Def1,Lm1;
A131:   z9 = z99 by A111,A129,XTUPLE_0:1;
A132:   +(y,z) = y9 -' z9 by A112,A126,ARYTM_1:def 2;
        then consider x9,yz9 being Element of REAL+ such that
A133:   x = [0,x9] and
A134:   +(y,z) = yz9 and
A135:   +(x,+(y,z)) = yz9 - x9 by A107,Def1;
A136:   x9 = x99 by A113,A133,XTUPLE_0:1;
        yz9 <=' y9 by A132,A134,ARYTM_1:11;
        then not x9 <=' yz9 by A110,A114,A125,A136,ARYTM_1:3;
        hence +(x,+(y,z)) = [0,x9 -' (y9 -' z9)] by A132,A134,A135,
ARYTM_1:def 2
          .= [0,x99 -' y99 + z99] by A110,A114,A125,A126,A136,A131,ARYTM_1:14
          .= +(+(x,y),z) by A128,A130,XTUPLE_0:1;
      end;
      suppose that
A137:   not z9 <=' y9 and
A138:   x99 <=' y99;
A139:   not(x in REAL+ & +(z,y) in [:{0},REAL+:]) by A107,Th5,XBOOLE_0:3;
A140:   +(y,z) = [0,z9 -' y9] by A112,A137,ARYTM_1:def 2;
        then +(y,z) in [:{0},REAL+:] by Lm1;
        then not(+(z,y) in REAL+ & x in [:{0},REAL+:]) by Th5,XBOOLE_0:3;
        then consider x9,yz99 being Element of REAL+ such that
A141:   x = [0,x9] and
A142:   +(y,z) = [0,yz99] & +(x,+(y,z)) = [0,x9 + yz99] by A140,A139,Def1,Lm1;
A143:   x99 = x9 by A113,A141,XTUPLE_0:1;
A144:   +(y,x) = y99 -' x99 by A115,A138,ARYTM_1:def 2;
        then consider z99,yx99 being Element of REAL+ such that
A145:   z = [0,z99] and
A146:   +(y,x) = yx99 and
A147:   +(z,+(y,x)) = yx99 - z99 by A109,Def1;
A148:   z99 = z9 by A111,A145,XTUPLE_0:1;
        yx99 <=' y99 by A144,A146,ARYTM_1:11;
        then
A149:   not z99 <=' yx99 by A110,A114,A137,A148,ARYTM_1:3;
        thus +(x,+(y,z)) = [0,z9 -' y9 + x9] by A140,A142,XTUPLE_0:1
          .= [0,z99 -' (y99 -' x99)] by A110,A114,A137,A138,A148,A143,
ARYTM_1:14
          .= +(+(x,y),z) by A144,A146,A147,A149,ARYTM_1:def 2;
      end;
      suppose that
A150:   not x99 <=' y99 and
A151:   not z9 <=' y9;
A152:   not(x in REAL+ & +(z,y) in [:{0},REAL+:]) by A107,Th5,XBOOLE_0:3;
A153:   not(z in REAL+ & +(x,y) in [:{0},REAL+:]) by A109,Th5,XBOOLE_0:3;
A154:   +(y,x) = [0,x99 -' y99] by A115,A150,ARYTM_1:def 2;
        then +(y,x) in [:{0},REAL+:] by Lm1;
        then not(+(x,y) in REAL+ & z in [:{0},REAL+:]) by Th5,XBOOLE_0:3;
        then consider z99,yx9 being Element of REAL+ such that
A155:   z = [0,z99] and
A156:   +(y,x) = [0,yx9] & +(z,+(y,x)) = [0,z99 + yx9] by A154,A153,Def1,Lm1;
A157:   z9 = z99 by A111,A155,XTUPLE_0:1;
A158:   +(y,z) = [0,z9 -' y9] by A112,A151,ARYTM_1:def 2;
        then +(y,z) in [:{0},REAL+:] by Lm1;
        then not(+(z,y) in REAL+ & x in [:{0},REAL+:]) by Th5,XBOOLE_0:3;
        then consider x9,yz99 being Element of REAL+ such that
A159:   x = [0,x9] and
A160:   +(y,z) = [0,yz99] & +(x,+(y,z)) = [0,x9 + yz99] by A158,A152,Def1,Lm1;
A161:   x9 = x99 by A113,A159,XTUPLE_0:1;
        thus +(x,+(y,z)) = [0,z9 -' y9 + x9] by A158,A160,XTUPLE_0:1
          .= [0,x99 -' y99 + z99] by A110,A114,A150,A151,A157,A161,ARYTM_1:15
          .= +(+(x,y),z) by A154,A156,XTUPLE_0:1;
      end;
    end;
    hence thesis;
  end;
  suppose that
A162: z in REAL+ and
A163: y in [:{0},REAL+:] and
A164: x in [:{0},REAL+:];
    ( not(x in REAL+ & y in [:{0},REAL+:]))& not(y in REAL+ & x in [:{0}
    ,REAL+:]) by A163,A164,Th5,XBOOLE_0:3;
    then consider y9,x9 being Element of REAL+ such that
A165: y = [0,y9] and
A166: x = [0,x9] and
A167: +(y,x) = [0,y9 + x9] by A163,Def1;
    +(y,x) in [:{0},REAL+:] by A167,Lm1;
    then consider z9,yx9 being Element of REAL+ such that
A168: z = z9 and
A169: +(y,x) = [0,yx9] and
A170: +(z,+(y,x)) = z9 - yx9 by A162,Def1;
    consider z99,y99 being Element of REAL+ such that
A171: z = z99 and
A172: y = [0,y99] and
A173: +(z,y) = z99 - y99 by A162,A163,Def1;
A174: y9 = y99 by A165,A172,XTUPLE_0:1;
    now
      per cases;
      suppose
A175:   y99 <=' z99;
        then
A176:   +(z,y) = z99 -' y99 by A173,ARYTM_1:def 2;
        then consider zy99,x99 being Element of REAL+ such that
A177:   +(z,y) = zy99 and
A178:   x = [0,x99] and
A179:   +(+(z,y),x) = zy99 - x99 by A164,Def1;
A180:   x9 = x99 by A166,A178,XTUPLE_0:1;
        thus +(z,+(y,x)) = z9 - (y9 + x9) by A167,A169,A170,XTUPLE_0:1
          .= +(+(z,y),x) by A171,A168,A174,A175,A176,A177,A179,A180,ARYTM_1:24;
      end;
      suppose
A181:   not y99 <=' z99;
A182:   not(x in REAL+ & +(z,y) in [:{0},REAL+:]) by A164,Th5,XBOOLE_0:3;
A183:   +(z,y) = [0,y99 -' z99] by A173,A181,ARYTM_1:def 2;
        then +(z,y) in [:{0},REAL+:] by Lm1;
        then not(+(z,y) in REAL+ & x in [:{0},REAL+:]) by Th5,XBOOLE_0:3;
        then consider zy99,x99 being Element of REAL+ such that
A184:   +(z,y) = [0,zy99] and
A185:   x = [0,x99] and
A186:   +(+(z,y),x) = [0,zy99 + x99] by A183,A182,Def1,Lm1;
A187:   x9 = x99 by A166,A185,XTUPLE_0:1;
A188:   yx9 = x9 + y9 by A167,A169,XTUPLE_0:1;
        then y99 <=' yx9 by A174,ARYTM_2:19;
        then not yx9 <=' z9 by A171,A168,A181,ARYTM_1:3;
        hence +(z,+(y,x)) = [0,x9 + y9 -' z9] by A170,A188,ARYTM_1:def 2
          .= [0,x99 + (y99 -' z99)] by A171,A168,A174,A181,A187,ARYTM_1:13
          .= +(+(z,y),x) by A183,A184,A186,XTUPLE_0:1;
      end;
    end;
    hence thesis;
  end;
  suppose that
A189: x in [:{0},REAL+:] and
A190: y in [:{0},REAL+:] and
A191: z in [:{0},REAL+:];
A192: not(x in REAL+ & +(z,y) in [:{0},REAL+:]) by A189,Th5,XBOOLE_0:3;
    ( not(z in REAL+ & y in [:{0},REAL+:]))& not(y in REAL+ & z in [:{0}
    ,REAL+:]) by A190,A191,Th5,XBOOLE_0:3;
    then consider y9,z9 being Element of REAL+ such that
A193: y = [0,y9] and
A194: z = [0,z9] and
A195: +(y,z) = [0,y9 + z9] by A190,Def1;
    +(z,y) in [:{0},REAL+:] by A195,Lm1;
    then not(+(z,y) in REAL+ & x in [:{0},REAL+:]) by Th5,XBOOLE_0:3;
    then consider x9,yz9 being Element of REAL+ such that
A196: x = [0,x9] and
A197: +(y,z) = [0,yz9] & +(x,+(y,z)) = [0,x9 + yz9] by A195,A192,Def1,Lm1;
A198: not(z in REAL+ & +(x,y) in [:{0},REAL+:]) by A191,Th5,XBOOLE_0:3;
    ( not(x in REAL+ & y in [:{0},REAL+:]))& not(y in REAL+ & x in [:{0}
    ,REAL+:]) by A189,A190,Th5,XBOOLE_0:3;
    then consider x99,y99 being Element of REAL+ such that
A199: x = [0,x99] and
A200: y = [0,y99] and
A201: +(x,y) = [0,x99 + y99] by A189,Def1;
A202: x9 = x99 by A199,A196,XTUPLE_0:1;
    +(x,y) in [:{0},REAL+:] by A201,Lm1;
    then not(+(x,y) in REAL+ & z in [:{0},REAL+:]) by Th5,XBOOLE_0:3;
    then consider xy99,z99 being Element of REAL+ such that
A203: +(x,y) = [0,xy99] and
A204: z = [0,z99] and
A205: +(+(x,y),z) = [0,xy99 + z99] by A201,A198,Def1,Lm1;
A206: z9 = z99 by A194,A204,XTUPLE_0:1;
A207: y9 = y99 by A193,A200,XTUPLE_0:1;
    thus +(x,+(y,z)) = [0,z9 + y9 + x9] by A195,A197,XTUPLE_0:1
      .= [0,z99 + (y99 + x99)] by A206,A202,A207,ARYTM_2:6
      .= +(+(x,y),z) by A201,A203,A205,XTUPLE_0:1;
  end;
end;
