const SNo : set prop const add_SNo : set set set term + = add_SNo infix + 2281 2280 axiom SNo_add_SNo_3: !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> SNo (x + y + z) axiom SNo_add_SNo: !x:set.!y:set.SNo x -> SNo y -> SNo (x + y) axiom add_SNo_com: !x:set.!y:set.SNo x -> SNo y -> x + y = y + x axiom add_SNo_com_4_inner_mid: !x:set.!y:set.!z:set.!w:set.SNo x -> SNo y -> SNo z -> SNo w -> (x + y) + z + w = (x + z) + y + w claim !x:set.!y:set.!z:set.!w:set.!u:set.SNo x -> SNo y -> SNo z -> SNo w -> SNo u -> (x + y + z) + w + u = (u + y + z) + w + x