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