equal
deleted
inserted
replaced
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 |