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