--- a/agda/automaton.agda	Thu Oct 17 20:00:26 2019 +0900
+++ b/agda/automaton.agda	Wed Oct 23 12:51:29 2019 +0900
@@ -4,9 +4,10 @@
 open import Data.Nat
 open import Data.List
 open import Data.Maybe
-open import Data.Bool using ( Bool ; true ; false ; _∧_ )
-open import  Relation.Binary.PropositionalEquality hiding ( [_] )
+-- open import Data.Bool using ( Bool ; true ; false ; _∧_ )
+open import Relation.Binary.PropositionalEquality hiding ( [_] )
 open import Relation.Nullary using (¬_; Dec; yes; no)
+open import logic
 
 record Automaton ( Q : Set ) ( Σ : Set  )
        : Set  where

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/agda/logic.agda	Wed Oct 23 12:51:29 2019 +0900
@@ -0,0 +1,50 @@
+module logic where
+
+open import Level
+open import Relation.Nullary
+open import Relation.Binary
+open import Data.Empty
+
+
+data Bool : Set where
+   true : Bool
+   false : Bool
+
+record  _∧_  {n m : Level} (A  : Set n) ( B : Set m ) : Set (n ⊔ m) where
+   field
+      proj1 : A
+      proj2 : B
+
+data  _∨_  {n m : Level} (A  : Set n) ( B : Set m ) : Set (n ⊔ m) where
+   case1 : A → A ∨ B
+   case2 : B → A ∨ B
+
+_⇔_ : {n m : Level } → ( A : Set n ) ( B : Set m )  → Set (n ⊔ m)
+_⇔_ A B =  ( A → B ) ∧ ( B → A )
+
+contra-position : {n m : Level } {A : Set n} {B : Set m} → (A → B) → ¬ B → ¬ A
+contra-position {n} {m} {A} {B}  f ¬b a = ¬b ( f a )
+
+double-neg : {n  : Level } {A : Set n} → A → ¬ ¬ A
+double-neg A notnot = notnot A
+
+double-neg2 : {n  : Level } {A : Set n} → ¬ ¬ ¬ A → ¬ A
+double-neg2 notnot A = notnot ( double-neg A )
+
+de-morgan : {n  : Level } {A B : Set n} →  A ∧ B  → ¬ ( (¬ A ) ∨ (¬ B ) )
+de-morgan {n} {A} {B} and (case1 ¬A) = ⊥-elim ( ¬A ( _∧_.proj1 and ))
+de-morgan {n} {A} {B} and (case2 ¬B) = ⊥-elim ( ¬B ( _∧_.proj2 and ))
+
+dont-or :　{n m : Level} {A  : Set n} { B : Set m } →  A ∨ B → ¬ A → B
+dont-or {A} {B} (case1 a) ¬A = ⊥-elim ( ¬A a )
+dont-or {A} {B} (case2 b) ¬A = b
+
+dont-orb :　{n m : Level} {A  : Set n} { B : Set m } →  A ∨ B → ¬ B → A
+dont-orb {A} {B} (case2 b) ¬B = ⊥-elim ( ¬B b )
+dont-orb {A} {B} (case1 a) ¬B = a
+
+
+infixr  130 _∧_
+infixr  140 _∨_
+infixr  150 _⇔_
+