[STATEMENT]
lemma arith_prog_dvd_mono: "b dvd b' \<Longrightarrow> arith_prog a b' \<subseteq> arith_prog a b"
[PROOF STATE]
proof (prove)
goal (1 subgoal):
 1. b dvd b' \<Longrightarrow> arith_prog a b' \<subseteq> arith_prog a b
[PROOF STEP]
by (auto simp: arith_prog_def cong_dvd_modulus)