let IT, IT' be BinOp of [:(Fin A),(Fin A):]; :: thesis: ( ( for a, b being Element of [:(Fin A),(Fin A):] holds IT . a,b = a \ b ) & ( for a, b being Element of [:(Fin A),(Fin A):] holds IT' . a,b = a \ b ) implies IT = IT' )
assume that
A1: for a, b being Element of [:(Fin A),(Fin A):] holds IT . a,b = a \ b and
A2: for a, b being Element of [:(Fin A),(Fin A):] holds IT' . a,b = a \ b ; :: thesis: IT = IT'

now

let a, b be Element of [:(Fin A),(Fin A):]; :: thesis: IT . a,b = IT' . a,b
IT . a,b = a \ b by A1;
hence IT . a,b = IT' . a,b by A2; :: thesis: verum

end;

hence IT = IT' by BINOP_1:2; :: thesis: verum