src/HOL/Nat_Transfer.thy
changeset 66795 420d0080545f
parent 64272 f76b6dda2e56
child 66817 0b12755ccbb2
equal deleted inserted replaced
66794:83bf64da6938 66795:420d0080545f
   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)"