src/HOL/Computational_Algebra/Field_as_Ring.thy
changeset 70817 dd675800469d
parent 66838 17989f6bc7b2
child 71398 e0237f2eb49d
equal deleted inserted replaced
70816:5bc338cee4a0 70817:dd675800469d
    33 definition [simp]: "euclidean_size_real = (euclidean_size_field :: real \<Rightarrow> _)"
    33 definition [simp]: "euclidean_size_real = (euclidean_size_field :: real \<Rightarrow> _)"
    34 definition [simp]: "division_segment (x :: real) = 1"
    34 definition [simp]: "division_segment (x :: real) = 1"
    35 
    35 
    36 instance
    36 instance
    37   by standard
    37   by standard
    38     (simp_all add: dvd_field_iff divide_simps split: if_splits)
    38     (simp_all add: dvd_field_iff field_split_simps split: if_splits)
    39 
    39 
    40 end
    40 end
    41 
    41 
    42 instantiation real :: euclidean_ring_gcd
    42 instantiation real :: euclidean_ring_gcd
    43 begin
    43 begin
    64 definition [simp]: "euclidean_size_rat = (euclidean_size_field :: rat \<Rightarrow> _)"
    64 definition [simp]: "euclidean_size_rat = (euclidean_size_field :: rat \<Rightarrow> _)"
    65 definition [simp]: "division_segment (x :: rat) = 1"
    65 definition [simp]: "division_segment (x :: rat) = 1"
    66 
    66 
    67 instance
    67 instance
    68   by standard
    68   by standard
    69     (simp_all add: dvd_field_iff divide_simps split: if_splits)
    69     (simp_all add: dvd_field_iff field_split_simps split: if_splits)
    70 
    70 
    71 end
    71 end
    72 
    72 
    73 instantiation rat :: euclidean_ring_gcd
    73 instantiation rat :: euclidean_ring_gcd
    74 begin
    74 begin
    95 definition [simp]: "euclidean_size_complex = (euclidean_size_field :: complex \<Rightarrow> _)"
    95 definition [simp]: "euclidean_size_complex = (euclidean_size_field :: complex \<Rightarrow> _)"
    96 definition [simp]: "division_segment (x :: complex) = 1"
    96 definition [simp]: "division_segment (x :: complex) = 1"
    97 
    97 
    98 instance
    98 instance
    99   by standard
    99   by standard
   100     (simp_all add: dvd_field_iff divide_simps split: if_splits)
   100     (simp_all add: dvd_field_iff field_split_simps split: if_splits)
   101 
   101 
   102 end
   102 end
   103 
   103 
   104 instantiation complex :: euclidean_ring_gcd
   104 instantiation complex :: euclidean_ring_gcd
   105 begin
   105 begin