Proving Reliability of Image Processing Techniques in Digital Forensics Applications

Listing 26

Proof of lemma distcb_eq_0.

	Lemma distcb_eq_0: for all p q, eqpixel p q = true->citydist p q = 0.
	Proof.
	intros.
	destruct p as [r1 c1 col1].
	destruct q as [r2 c2 col2].
	simpl.
	unfold eqpixel in .
	do 2 rewrite andb_true_iff in H.
	inversion H.
	inversion H0.
	assert (r1 = r2) as Hreq.
	apply beq_nat_true; auto.
	assert (c1 = c2) as Hceq.
	apply beq_nat_true; auto.
	rewrite Hreq. rewrite Hceq.
	unfold modminus.
	destruct ltb.
	destruct ltb.
	lia.
	lia.
	destruct ltb.
	lia.
	lia.
	Qed.