set A = the non empty set ;
set a = the BinOp of the non empty set ;
set Z = the Element of the non empty set ;
set l = the Function of [: the carrier of FS1, the non empty set :], the non empty set ;
set r = the Function of [: the non empty set , the carrier of FS2:], the non empty set ;
take BiModStr(# the non empty set , the BinOp of the non empty set , the Element of the non empty set , the Function of [: the carrier of FS1, the non empty set :], the non empty set , the Function of [: the non empty set , the carrier of FS2:], the non empty set #) ; :: thesis: not BiModStr(# the non empty set , the BinOp of the non empty set , the Element of the non empty set , the Function of [: the carrier of FS1, the non empty set :], the non empty set , the Function of [: the non empty set , the carrier of FS2:], the non empty set #) is empty
thus not the carrier of BiModStr(# the non empty set , the BinOp of the non empty set , the Element of the non empty set , the Function of [: the carrier of FS1, the non empty set :], the non empty set , the Function of [: the non empty set , the carrier of FS2:], the non empty set #) is empty ; :: according to STRUCT_0:def 1 :: thesis: verum