theorem Th25:
  FinMeet B "\/" p = FinMeet (((the L_join of DL)[:](id DL,p)).:B)
proof
  set J = the L_join of DL;
  set M = the L_meet of DL;
  thus FinMeet B "\/" p = J.(M $$ (B,id DL),p) by LATTICE2:def 4
    .= M $$ (B,J [:] (id DL,p)) by Lm3
    .=FinMeet(B,J [:] (id DL,p)) by LATTICE2:def 4
    .= FinMeet (B,(id DL)*(J [:] (id DL,p))) by FUNCT_2:17
    .= FinMeet (((the L_join of DL)[:](id DL,p)).: B) by Th22;
end;
