set X = the non empty set ;
set m = the BinOp of the non empty set ;
set M = the Function of [:COMPLEX, the non empty set :], the non empty set ;
set u = the Element of the non empty set ;
take ComplexAlgebraStr(# the non empty set , the BinOp of the non empty set , the BinOp of the non empty set , the Function of [:COMPLEX, the non empty set :], the non empty set , the Element of the non empty set , the Element of the non empty set #) ; :: thesis: not ComplexAlgebraStr(# the non empty set , the BinOp of the non empty set , the BinOp of the non empty set , the Function of [:COMPLEX, the non empty set :], the non empty set , the Element of the non empty set , the Element of the non empty set #) is empty
thus not the carrier of ComplexAlgebraStr(# the non empty set , the BinOp of the non empty set , the BinOp of the non empty set , the Function of [:COMPLEX, the non empty set :], the non empty set , the Element of the non empty set , the Element of the non empty set #) is empty ; :: according to STRUCT_0:def 1 :: thesis: verum