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comparison CCC.agda @ 787:ca5eba647990

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Thu, 18 Apr 2019 20:07:22 +0900
parents a67959bcd44b
children 4e1e2f7199c8
comparison
equal deleted inserted replaced
786:287d25c87b60 787:ca5eba647990
28 e3c : {a b c : Obj A} → { h : Hom A c (a ∧ b) } → A [ < A [ π o h ] , A [ π' o h ] > ≈ h ] 28 e3c : {a b c : Obj A} → { h : Hom A c (a ∧ b) } → A [ < A [ π o h ] , A [ π' o h ] > ≈ h ]
29 π-cong : {a b c : Obj A} → { f f' : Hom A c a }{ g g' : Hom A c b } → A [ f ≈ f' ] → A [ g ≈ g' ] → A [ < f , g > ≈ < f' , g' > ] 29 π-cong : {a b c : Obj A} → { f f' : Hom A c a }{ g g' : Hom A c b } → A [ f ≈ f' ] → A [ g ≈ g' ] → A [ < f , g > ≈ < f' , g' > ]
30 -- closed 30 -- closed
31 e4a : {a b c : Obj A} → { h : Hom A (c ∧ b) a } → A [ A [ ε o < A [ (h *) o π ] , π' > ] ≈ h ] 31 e4a : {a b c : Obj A} → { h : Hom A (c ∧ b) a } → A [ A [ ε o < A [ (h *) o π ] , π' > ] ≈ h ]
32 e4b : {a b c : Obj A} → { k : Hom A c (a <= b ) } → A [ ( A [ ε o < A [ k o π ] , π' > ] ) * ≈ k ] 32 e4b : {a b c : Obj A} → { k : Hom A c (a <= b ) } → A [ ( A [ ε o < A [ k o π ] , π' > ] ) * ≈ k ]
33 *-cong : {a b c : Obj A} → { f f' : Hom A (a ∧ b) c } → A [ f ≈ f' ] → A [ f * ≈ f' * ]
33 34
34 e'2 : A [ ○ １ ≈ id1 A １ ] 35 e'2 : A [ ○ １ ≈ id1 A １ ]
35 e'2 = let open ≈-Reasoning A in begin 36 e'2 = let open ≈-Reasoning A in begin
36 ○ １ 37 ○ １
37 ≈↑⟨ e2 (id1 A １ ) ⟩ 38 ≈↑⟨ e2 (id1 A １ ) ⟩