src/HOL/Integ/IntDef.thy
changeset 14348 744c868ee0b7
parent 14341 a09441bd4f1e
child 14378 69c4d5997669
equal deleted inserted replaced
14347:1fff56703e29 14348:744c868ee0b7
   342   show "i - j = i + (-j)" by (simp add: zdiff_def)
   342   show "i - j = i + (-j)" by (simp add: zdiff_def)
   343   show "(i * j) * k = i * (j * k)" by (rule zmult_assoc)
   343   show "(i * j) * k = i * (j * k)" by (rule zmult_assoc)
   344   show "i * j = j * i" by (rule zmult_commute)
   344   show "i * j = j * i" by (rule zmult_commute)
   345   show "1 * i = i" by simp
   345   show "1 * i = i" by simp
   346   show "(i + j) * k = i * k + j * k" by (simp add: int_distrib)
   346   show "(i + j) * k = i * k + j * k" by (simp add: int_distrib)
   347   show "0 \<noteq> (1::int)" by (simp only: Zero_int_def One_int_def One_nat_def int_int_eq)
   347   show "0 \<noteq> (1::int)" 
       
   348     by (simp only: Zero_int_def One_int_def One_nat_def int_int_eq)
   348   assume eq: "k+i = k+j" 
   349   assume eq: "k+i = k+j" 
   349     hence "(-k + k) + i = (-k + k) + j" by (simp only: eq zadd_assoc)
   350     hence "(-k + k) + i = (-k + k) + j" by (simp only: eq zadd_assoc)
   350     thus "i = j" by simp
   351     thus "i = j" by simp
   351 qed
   352 qed
   352 
   353