consider A being non empty set , b1, b2, b3 being BinOp of A;
take QuantaleStr(# A,b1,b2,b3 #) ; :: thesis: not QuantaleStr(# A,b1,b2,b3 #) is empty
thus not the carrier of QuantaleStr(# A,b1,b2,b3 #) is empty ; :: according to STRUCT_0:def 1 :: thesis: verum