section \<open>Main HOL\<close>
theory Main
imports Predicate_Compile Quickcheck_Narrowing Extraction Nitpick BNF_Greatest_Fixpoint Filter Conditionally_Complete_Lattices
begin
text \<open>
Classical Higher-order Logic -- only ``Main'', excluding real and
complex numbers etc.
\<close>
no_notation
bot ("\<bottom>") and
top ("\<top>") and
inf (infixl "\<sqinter>" 70) and
sup (infixl "\<squnion>" 65) and
Inf ("\<Sqinter>_" [900] 900) and
Sup ("\<Squnion>_" [900] 900) and
ordLeq2 (infix "<=o" 50) and
ordLeq3 (infix "\<le>o" 50) and
ordLess2 (infix "<o" 50) and
ordIso2 (infix "=o" 50) and
card_of ("|_|") and
csum (infixr "+c" 65) and
cprod (infixr "*c" 80) and
cexp (infixr "^c" 90) and
convol ("\<langle>(_,/ _)\<rangle>")
hide_const (open)
czero cinfinite cfinite csum cone ctwo Csum cprod cexp image2 image2p vimage2p Gr Grp collect
fsts snds setl setr convol pick_middlep fstOp sndOp csquare relImage relInvImage Succ Shift
shift proj id_bnf
hide_fact (open) id_bnf_def type_definition_id_bnf_UNIV
no_syntax
"_INF1" :: "pttrns \<Rightarrow> 'b \<Rightarrow> 'b" ("(3\<Sqinter>_./ _)" [0, 10] 10)
"_INF" :: "pttrn \<Rightarrow> 'a set \<Rightarrow> 'b \<Rightarrow> 'b" ("(3\<Sqinter>_\<in>_./ _)" [0, 0, 10] 10)
"_SUP1" :: "pttrns \<Rightarrow> 'b \<Rightarrow> 'b" ("(3\<Squnion>_./ _)" [0, 10] 10)
"_SUP" :: "pttrn \<Rightarrow> 'a set \<Rightarrow> 'b \<Rightarrow> 'b" ("(3\<Squnion>_\<in>_./ _)" [0, 0, 10] 10)
end