let K, L be non empty LattStr ; :: thesis: ( LattStr(# the carrier of K, the L_join of K, the L_meet of K #) = LattStr(# the carrier of L, the L_join of L, the L_meet of L #) & K is join-absorbing implies L is join-absorbing )
assume that
A1: LattStr(# the carrier of K, the L_join of K, the L_meet of K #) = LattStr(# the carrier of L, the L_join of L, the L_meet of L #) and
A2: K is join-absorbing ; :: thesis: L is join-absorbing
L is join-absorbing
proof
let x, y be Element of L; :: according to LATTICES:def 9 :: thesis: x |^| (x |_| y) = x
reconsider x9 = x, y9 = y as Element of K by A1;
x9 "/\" (x9 "\/" y9) = x9 by A2;
hence x |^| (x |_| y) = x by A1; :: thesis: verum
end;
hence L is join-absorbing ; :: thesis: verum