src/HOL/NumberTheory/Finite2.thy
changeset 20217 25b068a99d2b
parent 19670 2e4a143c73c5
child 20369 7e03c3ed1a18
equal deleted inserted replaced
20216:f30b73385060 20217:25b068a99d2b
   177 qed
   177 qed
   178 
   178 
   179 lemma int_card_bdd_int_set_l_l: "0 < n ==>
   179 lemma int_card_bdd_int_set_l_l: "0 < n ==>
   180     int(card {x. 0 < x & x < n}) = n - 1"
   180     int(card {x. 0 < x & x < n}) = n - 1"
   181   apply (auto simp add: card_bdd_int_set_l_l)
   181   apply (auto simp add: card_bdd_int_set_l_l)
   182   apply (subgoal_tac "Suc 0 \<le> nat n")
       
   183    apply (auto simp add: zdiff_int [symmetric])
       
   184   apply (subgoal_tac "0 < nat n", arith)
       
   185   apply (simp add: zero_less_nat_eq)
       
   186   done
   182   done
   187 
   183 
   188 lemma int_card_bdd_int_set_l_le: "0 \<le> n ==>
   184 lemma int_card_bdd_int_set_l_le: "0 \<le> n ==>
   189     int(card {x. 0 < x & x \<le> n}) = n"
   185     int(card {x. 0 < x & x \<le> n}) = n"
   190   by (auto simp add: card_bdd_int_set_l_le)
   186   by (auto simp add: card_bdd_int_set_l_le)