let L be LATTICE; :: thesis: for a, b, c being Element of L st a <= c holds
a "\/" (b "/\" c) <= (a "\/" b) "/\" c
let a, b, c be Element of L; :: thesis: ( a <= c implies a "\/" (b "/\" c) <= (a "\/" b) "/\" c )
assume A1: a <= c ; :: thesis: a "\/" (b "/\" c) <= (a "\/" b) "/\" c
A2: ( b "/\" c <= c & b "/\" c <= b & a <= a ) by YELLOW_0:23;
then A3: a "\/" (b "/\" c) <= c by A1, YELLOW_0:22;
a "\/" (b "/\" c) <= a "\/" b by A2, YELLOW_3:3;
hence a "\/" (b "/\" c) <= (a "\/" b) "/\" c by A3, YELLOW_0:23; :: thesis: verum