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283 lemma transfer_int_nat_functions: |
283 lemma transfer_int_nat_functions: |
284 "(int x) + (int y) = int (x + y)" |
284 "(int x) + (int y) = int (x + y)" |
285 "(int x) * (int y) = int (x * y)" |
285 "(int x) * (int y) = int (x * y)" |
286 "tsub (int x) (int y) = int (x - y)" |
286 "tsub (int x) (int y) = int (x - y)" |
287 "(int x)^n = int (x^n)" |
287 "(int x)^n = int (x^n)" |
288 by (auto simp add: of_nat_mult tsub_def of_nat_power) |
288 by (auto simp add: tsub_def) |
289 |
289 |
290 lemma transfer_int_nat_function_closures: |
290 lemma transfer_int_nat_function_closures: |
291 "is_nat x \<Longrightarrow> is_nat y \<Longrightarrow> is_nat (x + y)" |
291 "is_nat x \<Longrightarrow> is_nat y \<Longrightarrow> is_nat (x + y)" |
292 "is_nat x \<Longrightarrow> is_nat y \<Longrightarrow> is_nat (x * y)" |
292 "is_nat x \<Longrightarrow> is_nat y \<Longrightarrow> is_nat (x * y)" |
293 "is_nat x \<Longrightarrow> is_nat y \<Longrightarrow> is_nat (tsub x y)" |
293 "is_nat x \<Longrightarrow> is_nat y \<Longrightarrow> is_nat (tsub x y)" |