Structure defCNFTheory

signature defCNFTheory =
sig
  type thm = Thm.thm
  
  (*  Definitions  *)
    val DEF_def : thm
    val OKDEF_def : thm
  
  (*  Theorems  *)
    val BIGSTEP : thm
    val CONSISTENCY : thm
    val DEF_SNOC : thm
    val FINAL_DEF : thm
    val OKDEF_SNOC : thm
    val OK_def : thm
    val OK_ind : thm
    val UNIQUE_def : thm
    val UNIQUE_ind : thm
  
  val defCNF_grammars : type_grammar.grammar * term_grammar.grammar
(*
   [rich_list] Parent theory of "defCNF"
   
   [DEF_def]  Definition
      
      ⊢ (∀v n. defCNF$DEF v n [] ⇔ T) ∧
        ∀v n x xs.
            defCNF$DEF v n (x::xs) ⇔
            defCNF$UNIQUE v n x ∧ defCNF$DEF v (SUC n) xs
   
   [OKDEF_def]  Definition
      
      ⊢ (∀n. defCNF$OKDEF n [] ⇔ T) ∧
        ∀n x xs.
            defCNF$OKDEF n (x::xs) ⇔
            defCNF$OK n x ∧ defCNF$OKDEF (SUC n) xs
   
   [BIGSTEP]  Theorem
      
      ⊢ ∀P Q R. (∀v. P v ⇒ (Q ⇔ R v)) ⇒ ((∃v. P v) ∧ Q ⇔ ∃v. P v ∧ R v)
   
   [CONSISTENCY]  Theorem
      
      ⊢ ∀n l. defCNF$OKDEF n l ⇒ ∃v. defCNF$DEF v n l
   
   [DEF_SNOC]  Theorem
      
      ⊢ ∀n x l v.
            defCNF$DEF v n (SNOC x l) ⇔
            defCNF$DEF v n l ∧ defCNF$UNIQUE v (n + LENGTH l) x
   
   [FINAL_DEF]  Theorem
      
      ⊢ ∀v n x. (v n ⇔ x) ⇔ (v n ⇔ x) ∧ defCNF$DEF v (SUC n) []
   
   [OKDEF_SNOC]  Theorem
      
      ⊢ ∀n x l.
            defCNF$OKDEF n (SNOC x l) ⇔
            defCNF$OKDEF n l ∧ defCNF$OK (n + LENGTH l) x
   
   [OK_def]  Theorem
      
      ⊢ (defCNF$OK n (conn,INL i,INL j) ⇔ i < n ∧ j < n) ∧
        (defCNF$OK n (conn,INL i,INR b) ⇔ i < n) ∧
        (defCNF$OK n (conn,INR a,INL j) ⇔ j < n) ∧
        (defCNF$OK n (conn,INR a,INR b) ⇔ T)
   
   [OK_ind]  Theorem
      
      ⊢ ∀P.
            (∀n conn i j. P n (conn,INL i,INL j)) ∧
            (∀n conn i b. P n (conn,INL i,INR b)) ∧
            (∀n conn a j. P n (conn,INR a,INL j)) ∧
            (∀n conn a b. P n (conn,INR a,INR b)) ⇒
            ∀v v1 v2 v3. P v (v1,v2,v3)
   
   [UNIQUE_def]  Theorem
      
      ⊢ (defCNF$UNIQUE v n (conn,INL i,INL j) ⇔ (v n ⇔ conn (v i) (v j))) ∧
        (defCNF$UNIQUE v n (conn,INL i,INR b) ⇔ (v n ⇔ conn (v i) b)) ∧
        (defCNF$UNIQUE v n (conn,INR a,INL j) ⇔ (v n ⇔ conn a (v j))) ∧
        (defCNF$UNIQUE v n (conn,INR a,INR b) ⇔ (v n ⇔ conn a b))
   
   [UNIQUE_ind]  Theorem
      
      ⊢ ∀P.
            (∀v n conn i j. P v n (conn,INL i,INL j)) ∧
            (∀v n conn i b. P v n (conn,INL i,INR b)) ∧
            (∀v n conn a j. P v n (conn,INR a,INL j)) ∧
            (∀v n conn a b. P v n (conn,INR a,INR b)) ⇒
            ∀v v1 v2 v3 v4. P v v1 (v2,v3,v4)
   
   
*)
end

HOL 4, Kananaskis-13