moved lemmas for orderings and lattices on predicates to corresponding theories, retaining declaration order of classical rules; tuned headings; tuned syntax
structure HOL =
struct
type 'a eq = {eq : 'a -> 'a -> bool};
fun eq (A_:'a eq) = #eq A_;
type 'a ord = {less_eq : 'a -> 'a -> bool, less : 'a -> 'a -> bool};
fun less_eq (A_:'a ord) = #less_eq A_;
fun less (A_:'a ord) = #less A_;
end; (*struct HOL*)
structure Codegen =
struct
fun less_eq (A1_, A2_) B_ (x1, y1) (x2, y2) =
HOL.less A2_ x1 x2 orelse HOL.eq A1_ x1 x2 andalso HOL.less_eq B_ y1 y2;
end; (*struct Codegen*)