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changeset 355:e7a7cab74ca1

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Tue, 18 Jul 2023 15:47:36 +0900
parents bc2cb1c6bc80
children bd5cd2692b49
files automaton-in-agda/src/finiteSetUtil.agda
diffstat 1 files changed, 5 insertions(+), 5 deletions(-) [+]
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line diff
--- a/automaton-in-agda/src/finiteSetUtil.agda	Tue Jul 18 10:48:40 2023 +0900
+++ b/automaton-in-agda/src/finiteSetUtil.agda	Tue Jul 18 15:47:36 2023 +0900
@@ -649,14 +649,14 @@
         ... | no nisb = ⊥-elim ( nisb record { a = b ; fa=c = lem33 } ) where
             lem33 : f b ≡ Q←F fa ( fromℕ< {0} 0<fa )
             lem33 = begin
-              f b ≡⟨ ? ⟩
-              Q←F fa ( F←Q fa (f b))  ≡⟨ sym (cong (λ k → Q←F fa k)  ( fromℕ<-toℕ _ ?)) ⟩
-              Q←F fa ( fromℕ< ? )  ≡⟨ ? ⟩
+              f b ≡⟨ sym (finiso→  fa _) ⟩
+              Q←F fa ( F←Q fa (f b))  ≡⟨ sym (cong (λ k → Q←F fa k)  ( fromℕ<-toℕ _ fin<n)) ⟩
+              Q←F fa ( fromℕ< fin<n )  ≡⟨ cong (λ k → Q←F fa k) (fromℕ<-cong _ _ (sym eq) fin<n 0<fa) ⟩
               Q←F fa ( fromℕ< {0} 0<fa ) ∎ where
                 open ≡-Reasoning
         lem32 (suc n) eq with <-cmp (finite fa) (suc n)
-        ... | tri< a ¬b ¬c = ?
-        ... | tri≈ ¬a b ¬c = ?
+        ... | tri< a ¬b ¬c = ⊥-elim ( nat-≡< (sym eq) (<-trans fin<n a) )
+        ... | tri≈ ¬a eq1 ¬c = ⊥-elim ( nat-≡< (sym eq) (subst (λ k → toℕ (F←Q fa (f b)) < k ) eq1 fin<n ))
         ... | tri> ¬a ¬b c with is-B (Q←F fa (fromℕ< c))
         ... | yes isb = ?
         ... | no nisb = ?