src/HOL/Divides.thy
changeset 59380 e7d237c2ce93
parent 59058 a78612c67ec0
child 59473 b0ac740fc510
equal deleted inserted replaced
59379:c7f6f01ede15 59380:e7d237c2ce93
   508 apply (subgoal_tac "y * k = -y * -k")
   508 apply (subgoal_tac "y * k = -y * -k")
   509  apply (erule ssubst, rule div_mult_self1_is_id)
   509  apply (erule ssubst, rule div_mult_self1_is_id)
   510  apply simp
   510  apply simp
   511 apply simp
   511 apply simp
   512 done
   512 done
       
   513 
       
   514 lemma div_minus[simp]:
       
   515   "\<lbrakk> z dvd x; z dvd y\<rbrakk> \<Longrightarrow> (x - y) div z = x div z - y div z"
       
   516 using div_add[where y = "- z" for z]
       
   517 by (simp add: dvd_neg_div)
   513 
   518 
   514 lemma div_minus_minus [simp]: "(-a) div (-b) = a div b"
   519 lemma div_minus_minus [simp]: "(-a) div (-b) = a div b"
   515   using div_mult_mult1 [of "- 1" a b]
   520   using div_mult_mult1 [of "- 1" a b]
   516   unfolding neg_equal_0_iff_equal by simp
   521   unfolding neg_equal_0_iff_equal by simp
   517 
   522