 reserve A for non empty Subset of REAL;
 reserve A for non empty closed_interval Subset of REAL;

theorem Lm22d:
  for a,b,c,d,r be Real st a < b & b < c & c < d holds
    r (#) TrapezoidalFS (a,b,c,d) is_integrable_on A
proof
 let a,b,c,d,r be Real;
 assume A1: a < b & b < c & c < d;
 reconsider f = TrapezoidalFS (a,b,c,d) as PartFunc of REAL,REAL;
 A2: f is_integrable_on A & f | A is bounded by Lm22c,A1;
 REAL = dom f by FUNCT_2:def 1;
 hence thesis by A2,INTEGRA6:9;
end;
