let L be non empty reflexive antisymmetric with_infima RelStr ; :: thesis: ( L is distributive implies L is modular )
assume A1: L is distributive ; :: thesis: L is modular

now

let a, b, c be Element of L; :: thesis: ( a <= c implies a "\/" (b "/\" c) = (a "\/" b) "/\" c )
assume a <= c ; :: thesis: a "\/" (b "/\" c) = (a "\/" b) "/\" c
hence a "\/" (b "/\" c) = (a "/\" c) "\/" (b "/\" c) by YELLOW_0:25
.= (a "\/" b) "/\" c by A1, WAYBEL_1:def 3 ;
:: thesis: verum

end;

hence L is modular by Def3; :: thesis: verum