src/HOL/GCD.thy
changeset 69038 2ce9bc515a64
parent 68796 9ca183045102
child 69064 5840724b1d71
equal deleted inserted replaced
69037:8d8fdbc02912 69038:2ce9bc515a64
  1090 context semiring_gcd
  1090 context semiring_gcd
  1091 begin
  1091 begin
  1092 
  1092 
  1093 sublocale Gcd_fin: bounded_quasi_semilattice_set gcd 0 1 normalize
  1093 sublocale Gcd_fin: bounded_quasi_semilattice_set gcd 0 1 normalize
  1094 defines
  1094 defines
  1095   Gcd_fin ("Gcd\<^sub>f\<^sub>i\<^sub>n _" [900] 900) = "Gcd_fin.F :: 'a set \<Rightarrow> 'a" ..
  1095   Gcd_fin ("Gcd\<^sub>f\<^sub>i\<^sub>n") = "Gcd_fin.F :: 'a set \<Rightarrow> 'a" ..
  1096 
  1096 
  1097 abbreviation gcd_list :: "'a list \<Rightarrow> 'a"
  1097 abbreviation gcd_list :: "'a list \<Rightarrow> 'a"
  1098   where "gcd_list xs \<equiv> Gcd\<^sub>f\<^sub>i\<^sub>n (set xs)"
  1098   where "gcd_list xs \<equiv> Gcd\<^sub>f\<^sub>i\<^sub>n (set xs)"
  1099 
  1099 
  1100 sublocale Lcm_fin: bounded_quasi_semilattice_set lcm 1 0 normalize
  1100 sublocale Lcm_fin: bounded_quasi_semilattice_set lcm 1 0 normalize
  1101 defines
  1101 defines
  1102   Lcm_fin ("Lcm\<^sub>f\<^sub>i\<^sub>n _" [900] 900) = Lcm_fin.F ..
  1102   Lcm_fin ("Lcm\<^sub>f\<^sub>i\<^sub>n") = Lcm_fin.F ..
  1103 
  1103 
  1104 abbreviation lcm_list :: "'a list \<Rightarrow> 'a"
  1104 abbreviation lcm_list :: "'a list \<Rightarrow> 'a"
  1105   where "lcm_list xs \<equiv> Lcm\<^sub>f\<^sub>i\<^sub>n (set xs)"
  1105   where "lcm_list xs \<equiv> Lcm\<^sub>f\<^sub>i\<^sub>n (set xs)"
  1106 
  1106 
  1107 lemma Gcd_fin_dvd:
  1107 lemma Gcd_fin_dvd: