diff -r 989182f660e0 -r 8a86fd2a1bf0 src/HOL/Library/Continuity.thy --- a/src/HOL/Library/Continuity.thy Fri Mar 16 21:32:07 2007 +0100 +++ b/src/HOL/Library/Continuity.thy Fri Mar 16 21:32:08 2007 +0100 @@ -12,15 +12,15 @@ subsection {* Continuity for complete lattices *} definition - chain :: "(nat \ 'a::order) \ bool" where + chain :: "(nat \ 'a::complete_lattice) \ bool" where "chain M \ (\i. M i \ M (Suc i))" definition - continuous :: "('a::comp_lat \ 'a::comp_lat) \ bool" where + continuous :: "('a::complete_lattice \ 'a::complete_lattice) \ bool" where "continuous F \ (\M. chain M \ F (SUP i. M i) = (SUP i. F (M i)))" abbreviation - bot :: "'a::order" where + bot :: "'a::complete_lattice" where "bot \ Sup {}" lemma SUP_nat_conv: @@ -34,7 +34,7 @@ apply (blast intro:SUP_leI le_SUPI) done -lemma continuous_mono: fixes F :: "'a::comp_lat \ 'a::comp_lat" +lemma continuous_mono: fixes F :: "'a::complete_lattice \ 'a::complete_lattice" assumes "continuous F" shows "mono F" proof fix A B :: "'a" assume "A <= B"