src/HOL/GCD.thy
changeset 54257 5c7a3b6b05a9
parent 52729 412c9e0381a1
child 54437 0060957404c7
     1.1 --- a/src/HOL/GCD.thy	Tue Nov 05 05:48:08 2013 +0100
     1.2 +++ b/src/HOL/GCD.thy	Tue Nov 05 09:44:57 2013 +0100
     1.3 @@ -1555,8 +1555,8 @@
     1.4  interpretation gcd_lcm_complete_lattice_nat:
     1.5    complete_lattice Gcd Lcm gcd Rings.dvd "\<lambda>m n. m dvd n \<and> \<not> n dvd m" lcm 1 "0::nat"
     1.6  where
     1.7 -  "complete_lattice.INFI Gcd A f = Gcd (f ` A :: nat set)"
     1.8 -  and "complete_lattice.SUPR Lcm A f = Lcm (f ` A)"
     1.9 +  "Inf.INFI Gcd A f = Gcd (f ` A :: nat set)"
    1.10 +  and "Sup.SUPR Lcm A f = Lcm (f ` A)"
    1.11  proof -
    1.12    show "class.complete_lattice Gcd Lcm gcd Rings.dvd (\<lambda>m n. m dvd n \<and> \<not> n dvd m) lcm 1 (0::nat)"
    1.13    proof
    1.14 @@ -1574,8 +1574,8 @@
    1.15    qed
    1.16    then interpret gcd_lcm_complete_lattice_nat:
    1.17      complete_lattice Gcd Lcm gcd Rings.dvd "\<lambda>m n. m dvd n \<and> \<not> n dvd m" lcm 1 "0::nat" .
    1.18 -  from gcd_lcm_complete_lattice_nat.INF_def show "complete_lattice.INFI Gcd A f = Gcd (f ` A)" .
    1.19 -  from gcd_lcm_complete_lattice_nat.SUP_def show "complete_lattice.SUPR Lcm A f = Lcm (f ` A)" .
    1.20 +  from gcd_lcm_complete_lattice_nat.INF_def show "Inf.INFI Gcd A f = Gcd (f ` A)" .
    1.21 +  from gcd_lcm_complete_lattice_nat.SUP_def show "Sup.SUPR Lcm A f = Lcm (f ` A)" .
    1.22  qed
    1.23  
    1.24  lemma Lcm_empty_nat: "Lcm {} = (1::nat)"