equal
deleted
inserted
replaced
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: |