let L be LATTICE; :: thesis: for a, b, c being Element of L holds a "\/" (b "/\" c) <= (a "\/" b) "/\" (a "\/" c)
let a, b, c be Element of L; :: thesis: a "\/" (b "/\" c) <= (a "\/" b) "/\" (a "\/" c)
A1: a <= a ;
b "/\" c <= c by YELLOW_0:23;
then A2: a "\/" (b "/\" c) <= a "\/" c by A1, YELLOW_3:3;
b "/\" c <= b by YELLOW_0:23;
then a "\/" (b "/\" c) <= a "\/" b by A1, YELLOW_3:3;
hence a "\/" (b "/\" c) <= (a "\/" b) "/\" (a "\/" c) by A2, YELLOW_0:23; :: thesis: verum