equal
deleted
inserted
replaced
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)" |
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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 |