Mercurial > hg > Members > kono > Proof > category
diff limit-to.agda @ 495:633df882db86
fryed1 done
author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
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date | Tue, 14 Mar 2017 13:08:03 +0900 |
parents | c257347a27f3 |
children | 3ce21b2a671a |
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--- a/limit-to.agda Tue Mar 14 12:14:57 2017 +0900 +++ b/limit-to.agda Tue Mar 14 13:08:03 2017 +0900 @@ -226,7 +226,7 @@ → A [ A [ e o k' ] ≈ h ] → A [ k h fh=gh ≈ k' ] uniquness d h fh=gh k' ek'=h = let open ≈-Reasoning A in begin k h fh=gh - ≈⟨ limit-uniqueness (isLimit lim) k' ( λ{i} → uniq-nat {i} d h k' fh=gh ek'=h ) ⟩ + ≈⟨ limit-uniqueness (isLimit lim) ( λ{i} → uniq-nat {i} d h k' fh=gh ek'=h ) ⟩ k' ∎ @@ -290,7 +290,7 @@ ipu : {i : Obj D} → (q : Obj A) (h : Hom A q p ) → A [ A [ TMap (limit-u comp Γ) i o h ] ≈ A [ pi i o h ] ] ipu {i} q h = let open ≈-Reasoning A in refl-hom ip-uniqueness : {q : Obj A} { h : Hom A q p } → A [ iproduct ( λ (i : I) → A [ (pi i) o h ] ) ≈ h ] - ip-uniqueness {q} {h} = limit-uniqueness (isLimit lim) {q} {pnat A S Γ (λ i → A [ pi i o h ] )} h (ipu q h) + ip-uniqueness {q} {h} = limit-uniqueness (isLimit lim) {q} {pnat A S Γ (λ i → A [ pi i o h ] )} (ipu q h) ipc : {q : Obj A} → { qi : (i : I) → Hom A q (ai i) } → { qi' : (i : I) → Hom A q (ai i) } → (i : I ) → A [ qi i ≈ qi' i ] → A [ A [ TMap (limit-u comp Γ) i o iproduct qi' ] ≈ TMap (pnat A S Γ qi) i ] @@ -309,4 +309,4 @@ ∎ ip-cong : {q : Obj A} → { qi : (i : I) → Hom A q (ai i) } → { qi' : (i : I) → Hom A q (ai i) } → ( ∀ (i : I ) → A [ qi i ≈ qi' i ] ) → A [ iproduct qi ≈ iproduct qi' ] - ip-cong {q} {qi} {qi'} qi=qi' = limit-uniqueness (isLimit lim) {q} {pnat A S Γ qi} (iproduct qi' ) (λ {i} → ipc {q} {qi} {qi'} i (qi=qi' i)) + ip-cong {q} {qi} {qi'} qi=qi' = limit-uniqueness (isLimit lim) {q} {pnat A S Γ qi} (λ {i} → ipc {q} {qi} {qi'} i (qi=qi' i))