reserve r, r1, r2, x, y, z,
        x1, x2, x3, y1, y2, y3 for Real;
reserve R, R1, R2, R3 for Element of 3-tuples_on REAL;
reserve p, q, p1, p2, p3, q1, q2 for Element of REAL 3;
reserve f1, f2, f3, g1, g2, g3, h1, h2, h3 for PartFunc of REAL,REAL;
reserve t, t0, t1, t2 for Real;

theorem
  (f1.t1 = g1.t2 & f2.t1 = g2.t2 & f3.t1 = g3.t2) implies
  VFunc(f1,f2,f3).t1 = VFunc(g1,g2,g3).t2
proof
    assume
A1: f1.t1 = g1.t2 & f2.t1 = g2.t2 & f3.t1 = g3.t2;
    set p = |[ f1.t1,f2.t1,f3.t1 ]|;
    set q = |[ g1.t2,g2.t2,g3.t2 ]|;
    p = VFunc(f1,f2,f3).t1 & q = VFunc(g1,g2,g3).t2 by Def5;
    hence thesis by A1;
end;
