const In : set set prop term iIn = In infix iIn 2000 2000 const SNoLev : set set const SNoL : set set const SNoLt : set set prop term < = SNoLt infix < 2020 2020 const add_SNo : set set set term + = add_SNo infix + 2281 2280 const mul_SNo : set set set term * = mul_SNo infix * 2291 2290 const SNo : set prop var x:set var y:set var z:set var w:set hyp SNo y hyp SNo w hyp w < y hyp !u:set.u iIn SNoL x -> !v:set.v iIn SNoL y -> (u * y + x * v) < x * y + u * v hyp z iIn SNoL x hyp SNoLev w iIn SNoLev y claim w iIn SNoL y -> (z * y + x * w) < x * y + z * w