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-associative implies L is meet-associative )
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 meet-associative ) ; :: thesis: L is meet-associative
L is meet-associative

proof

let x, y, z be Element of L; :: according to LATTICES:def 7 :: thesis: x |^| (y |^| z) = (x |^| y) |^| z
reconsider x' = x, y' = y, z' = z as Element of K by A1;
(x' "/\" y') "/\" z' = x' "/\" (y' "/\" z') by A1, LATTICES:def 7;
hence x |^| (y |^| z) = (x |^| y) |^| z by A1; :: thesis: verum

end;

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