let L be Lattice; :: thesis: for p, q, r being Element of L holds
( p is_greater_than {q,r} iff q "\/" r [= p )
let p, q, r be Element of L; :: thesis: ( p is_greater_than {q,r} iff q "\/" r [= p )
A1: ( q in {q,r} & r in {q,r} ) by TARSKI:def 2;
thus ( p is_greater_than {q,r} implies q "\/" r [= p ) :: thesis: ( q "\/" r [= p implies p is_greater_than {q,r} )

proof

assume p is_greater_than {q,r} ; :: thesis: q "\/" r [= p
then ( q [= p & r [= p ) by A1, Def17;
hence q "\/" r [= p by FILTER_0:6; :: thesis: verum

end;

assume A2: q "\/" r [= p ; :: thesis: p is_greater_than {q,r}
let a be Element of L; :: according to LATTICE3:def 17 :: thesis: ( a in {q,r} implies a [= p )
assume a in {q,r} ; :: thesis: a [= p
then ( ( a = q or a = r ) & q [= q "\/" r & r [= r "\/" q & q "\/" r = r "\/" q ) by LATTICES:22, TARSKI:def 2;
hence a [= p by A2, LATTICES:25; :: thesis: verum