reserve X for set, x,y,z for object,
  k,l,n for Nat,
  r for Real;
reserve i,i0,i1,i2,i3,i4,i5,i8,i9,j for Integer;
reserve r1,p,p1,g,g1,g2 for Real,
  Y for Subset of REAL;
reserve r, s for Real;
reserve i for Integer,
  a, b, r, s for Real;

theorem Th65:
  r <= a & a < [\r/]+1 implies [\a/] = [\r/]
proof
  assume
A1: r <= a;
  assume a < [\r/]+1;
  then
A2: a-1 < [\r/]+1-1 by XREAL_1:9;
  [\r/] <= r by Def6;
  then [\r/] <= a by A1,XXREAL_0:2;
  hence thesis by A2,Def6;
end;
