set A = the non empty set ;
set m = the BinOp of the non empty set ;
take MidStr(# the non empty set , the BinOp of the non empty set #) ; :: thesis: not MidStr(# the non empty set , the BinOp of the non empty set #) is empty
thus not the carrier of MidStr(# the non empty set , the BinOp of the non empty set #) is empty ; :: according to STRUCT_0:def 1 :: thesis: verum