let L be Semilattice; :: thesis: for x, y being Element of (InclPoset (Ids L))
for x1, y1 being Subset of L st x = x1 & y = y1 holds
x "/\" y = x1 "/\" y1
let x, y be Element of (InclPoset (Ids L)); :: thesis: for x1, y1 being Subset of L st x = x1 & y = y1 holds
x "/\" y = x1 "/\" y1
let x1, y1 be Subset of L; :: thesis: ( x = x1 & y = y1 implies x "/\" y = x1 "/\" y1 )
assume A1: ( x = x1 & y = y1 ) ; :: thesis: x "/\" y = x1 "/\" y1
then A2: ( x1 is lower & y1 is lower ) by YELLOW_2:41;
thus x "/\" y = x /\ y by YELLOW_2:43
.= x1 "/\" y1 by A1, A2, Th50 ; :: thesis: verum