ABSTRACT
Lemma 2.5. Let A C [0, H ] and 0 ^ x\ ^ xi ^ H be such that (1) (2A){2x \92x2) У 3A{x\,X2), (2) i f 0 -< x\, then A[ 0, x] is not a subset of an a.p. o f difference d ^ 2 and
A{0,x) ^ \{x + 1) for some x ~ x\, (3) i f X2 -< H , then A[x , H] is not a subset of an a.p. of difference d ^ 2 and
A(x, H ) < \ {H — x + 1) for some x ~ X2, Then (2A)(0,2H) У 3A(0,H).
