src/HOL/Decision_Procs/MIR.thy
changeset 63600 d0fa16751d14
parent 62342 1cf129590be8
child 64240 eabf80376aab
equal deleted inserted replaced
63599:f560147710fb 63600:d0fa16751d14
  1524   have th': "(real_of_int ?nt)*(real_of_int x) = real_of_int (?nt * x)" by simp
  1524   have th': "(real_of_int ?nt)*(real_of_int x) = real_of_int (?nt * x)" by simp
  1525   have "?I x (Floor t) = ?I x (Floor (CN 0 ?nt ?at))" using th2 by simp
  1525   have "?I x (Floor t) = ?I x (Floor (CN 0 ?nt ?at))" using th2 by simp
  1526   also have "\<dots> = real_of_int \<lfloor>real_of_int ?nt * real_of_int x + ?I x ?at\<rfloor>" by simp
  1526   also have "\<dots> = real_of_int \<lfloor>real_of_int ?nt * real_of_int x + ?I x ?at\<rfloor>" by simp
  1527   also have "\<dots> = real_of_int \<lfloor>?I x ?at + real_of_int (?nt * x)\<rfloor>" by (simp add: ac_simps)
  1527   also have "\<dots> = real_of_int \<lfloor>?I x ?at + real_of_int (?nt * x)\<rfloor>" by (simp add: ac_simps)
  1528   also have "\<dots> = real_of_int (\<lfloor>?I x ?at\<rfloor> + (?nt * x))"
  1528   also have "\<dots> = real_of_int (\<lfloor>?I x ?at\<rfloor> + (?nt * x))"
  1529     using floor_add_of_int[of "?I x ?at" "?nt * x"] by simp
  1529     by (simp add: of_int_mult[symmetric] del: of_int_mult)
  1530   also have "\<dots> = real_of_int (?nt)*(real_of_int x) + real_of_int \<lfloor>?I x ?at\<rfloor>" by (simp add: ac_simps)
  1530   also have "\<dots> = real_of_int (?nt)*(real_of_int x) + real_of_int \<lfloor>?I x ?at\<rfloor>" by (simp add: ac_simps)
  1531   finally have "?I x (Floor t) = ?I x (CN 0 n a)" using th by simp
  1531   finally have "?I x (Floor t) = ?I x (CN 0 n a)" using th by simp
  1532   with na show ?case by simp
  1532   with na show ?case by simp
  1533 qed
  1533 qed
  1534 
  1534