If you need the definition of S further down in the proof, you may prefer the variant<4>1. J \in Nat<4>. DEFINE S == ( 0 .. 9 ) \X ( 0 .. 9 ) \X ( ( 0 .. 9 ) \X ( 0 .. 9 ) )<4>2. seq \in [ 1 .. J -> S]<4>3. seq \in Seq(S)<5>. HIDE DEF S<5>. QED BY <4>1, <4>2