 reserve S for satisfying_Tarski-model TarskiGeometryStruct;
 reserve a, b, c, d, e, f, o, p, q, r, s,
    v, w, u, x, y, z, a9, b9, c9, d9, x9, y9, z for POINT of S;

theorem C1:
  a <> b & between a,b,x & between a,b,y & b,x equiv b,y
    implies x = y
  proof
    assume that
H1: a <> b and
H2: between a,b,x & between a,b,y and
H3: b,x equiv b,y;
    a,b,y cong a,b,y by EquivReflexive;
    hence y = x by A3, H1, H2, H3, A5;
  end;
