reserve i,j,k,n for Nat;
reserve x,y,z for Tuple of n, BOOLEAN;

theorem Th4:
  for b1,b2,c being Nat holds b2 <= c implies b2 - b1 <= c
proof
  let b1,b2,c be Nat;
  assume b2 <= c;
  then
A1: b2 - b1 <= c - b1 by XREAL_1:9;
  c - b1 <= c by Th3;
  hence thesis by A1,XXREAL_0:2;
end;
