reserve MS for OrtAfPl;
reserve MP for OrtAfSp;

theorem
  for a,b being Element of MS, A,K being Subset of the carrier of MS st
  a<>b & (a,b _|_ K or b,a _|_ K) & a,b _|_ A holds K // A
proof
  let a,b be Element of MS, A,K be Subset of MS such that
A1: a<>b and
A2: a,b _|_ K or b,a _|_ K and
A3: a,b _|_ A;
  a,b _|_ K by A2,ANALMETR:49;
  then consider p,q being Element of MS such that
A4: p<>q & K = Line(p,q) and
A5: a,b _|_ p,q by ANALMETR:def 13;
  consider r,s being Element of MS such that
A6: r<>s & A = Line(r,s) and
A7: a,b _|_ r,s by A3,ANALMETR:def 13;
  p,q // r,s by A1,A5,A7,ANALMETR:63;
  hence thesis by A4,A6,ANALMETR:def 15;
end;
