let C be complete Lattice; :: thesis: for a being Element of C
for X being set st a in X & X is_less_than a holds
"\/" X,C = a
let a be Element of C; :: thesis: for X being set st a in X & X is_less_than a holds
"\/" X,C = a
let X be set ; :: thesis: ( a in X & X is_less_than a implies "\/" X,C = a )
assume ( a in X & X is_less_than a ) ; :: thesis: "\/" X,C = a
then ( "\/" X,C [= a & a [= "\/" X,C ) by Def21, Th38;
hence "\/" X,C = a by LATTICES:26; :: thesis: verum