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 meet-absorbing implies L is meet-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 meet-absorbing ; :: thesis: L is meet-absorbing
L is meet-absorbing

proof

let x, y be Element of L; :: according to LATTICES:def 8 :: thesis: (x |^| y) |_| y = y
reconsider x9 = x, y9 = y as Element of K by A1;
(x9 "/\" y9) "\/" y9 = y9 by A2;
hence (x |^| y) |_| y = y by A1; :: thesis: verum

end;

hence L is meet-absorbing ; :: thesis: verum