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 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 #) & 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 x' = x, y' = y as Element of K by A1;
x' "/\" (x' "\/" y') = x' by A1, LATTICES:def 9;
hence x |^| (x |_| y) = x by A1; :: thesis: verum

end;

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