src/HOL/Main.thy

Some new lemmas and some tidying

section \<open>Main HOL\<close>

text \<open>
  Classical Higher-order Logic -- only ``Main'', excluding real and
  complex numbers etc.
\<close>

theory Main
  imports
    Predicate_Compile
    Quickcheck_Narrowing
    Mirabelle
    Extraction
    Nunchaku
    BNF_Greatest_Fixpoint
    Filter
    Conditionally_Complete_Lattices
    Binomial
    GCD
begin

subsection \<open>Namespace cleanup\<close>

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


subsection \<open>Syntax cleanup\<close>

no_notation
  ordLeq2 (infix \<open><=o\<close> 50) and
  ordLeq3 (infix \<open>\<le>o\<close> 50) and
  ordLess2 (infix \<open><o\<close> 50) and
  ordIso2 (infix \<open>=o\<close> 50) and
  card_of (\<open>(\<open>open_block notation=\<open>mixfix card_of\<close>\<close>|_|)\<close>) and
  BNF_Cardinal_Arithmetic.csum (infixr \<open>+c\<close> 65) and
  BNF_Cardinal_Arithmetic.cprod (infixr \<open>*c\<close> 80) and
  BNF_Cardinal_Arithmetic.cexp (infixr \<open>^c\<close> 90) and
  BNF_Def.convol (\<open>(\<open>indent=1 notation=\<open>mixfix convol\<close>\<close>\<langle>_,/ _\<rangle>)\<close>)

bundle cardinal_syntax
begin

notation
  ordLeq2 (infix \<open><=o\<close> 50) and
  ordLeq3 (infix \<open>\<le>o\<close> 50) and
  ordLess2 (infix \<open><o\<close> 50) and
  ordIso2 (infix \<open>=o\<close> 50) and
  card_of (\<open>(\<open>open_block notation=\<open>mixfix card_of\<close>\<close>|_|)\<close>) and
  BNF_Cardinal_Arithmetic.csum (infixr \<open>+c\<close> 65) and
  BNF_Cardinal_Arithmetic.cprod (infixr \<open>*c\<close> 80) and
  BNF_Cardinal_Arithmetic.cexp (infixr \<open>^c\<close> 90)

alias cinfinite = BNF_Cardinal_Arithmetic.cinfinite
alias czero = BNF_Cardinal_Arithmetic.czero
alias cone = BNF_Cardinal_Arithmetic.cone
alias ctwo = BNF_Cardinal_Arithmetic.ctwo

end


subsection \<open>Lattice syntax\<close>

bundle lattice_syntax
begin

notation
  bot  (\<open>\<bottom>\<close>) and
  top  (\<open>\<top>\<close>) and
  inf  (infixl \<open>\<sqinter>\<close> 70) and
  sup  (infixl \<open>\<squnion>\<close> 65) and
  Inf  (\<open>(\<open>open_block notation=\<open>prefix \<Sqinter>\<close>\<close>\<Sqinter> _)\<close> [900] 900) and
  Sup  (\<open>(\<open>open_block notation=\<open>prefix \<Squnion>\<close>\<close>\<Squnion> _)\<close> [900] 900)

syntax
  "_INF1"     :: "pttrns \<Rightarrow> 'b \<Rightarrow> 'b"           (\<open>(\<open>indent=3 notation=\<open>binder \<Sqinter>\<close>\<close>\<Sqinter>_./ _)\<close> [0, 10] 10)
  "_INF"      :: "pttrn \<Rightarrow> 'a set \<Rightarrow> 'b \<Rightarrow> 'b"  (\<open>(\<open>indent=3 notation=\<open>binder \<Sqinter>\<close>\<close>\<Sqinter>_\<in>_./ _)\<close> [0, 0, 10] 10)
  "_SUP1"     :: "pttrns \<Rightarrow> 'b \<Rightarrow> 'b"           (\<open>(\<open>indent=3 notation=\<open>binder \<Squnion>\<close>\<close>\<Squnion>_./ _)\<close> [0, 10] 10)
  "_SUP"      :: "pttrn \<Rightarrow> 'a set \<Rightarrow> 'b \<Rightarrow> 'b"  (\<open>(\<open>indent=3 notation=\<open>binder \<Squnion>\<close>\<close>\<Squnion>_\<in>_./ _)\<close> [0, 0, 10] 10)

end

unbundle no lattice_syntax

end