let L be LATTICE; :: thesis: for a, b, c being Element of L holds (a "/\" b) "\/" (a "/\" c) <= a "/\" (b "\/" c)
let a, b, c be Element of L; :: thesis: (a "/\" b) "\/" (a "/\" c) <= a "/\" (b "\/" c)
A1: a <= a ;
c <= b "\/" c by YELLOW_0:22;
then A2: a "/\" c <= a "/\" (b "\/" c) by A1, YELLOW_3:2;
b <= b "\/" c by YELLOW_0:22;
then a "/\" b <= a "/\" (b "\/" c) by A1, YELLOW_3:2;
hence (a "/\" b) "\/" (a "/\" c) <= a "/\" (b "\/" c) by A2, YELLOW_5:9; :: thesis: verum