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Beat head against the vector-cast wall.

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin 2024-04-07 23:44:35 -07:00
parent b72ad070ba
commit f7ac22257e
1 changed files with 16 additions and 1 deletions
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17
Language.agda
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@ -121,10 +121,25 @@ module Graphs where
e ∈ˡ (Graph.edges g₁) →
(↑ˡ-Edge e n) ∈ˡ (subst (λ m → List (Fin m × Fin m)) sg₂≡sg₁+n (Graph.edges g₂))
⊆-trans : ∀ {g₁ g₂ g₃ : Graph} → g₁ ⊆ g₂ → g₂ ⊆ g₃ → g₁ ⊆ g₃
⊆-trans {MkGraph s₁ ns₁ es₁} {MkGraph s₂ ns₂ es₂} {MkGraph s₃ ns₃ es₃} (Mk-⊆ n₁ p₁@refl g₁[]≡g₂[] e∈g₁⇒e∈g₂) (Mk-⊆ n₂ p₂@refl g₂[]≡g₃[] e∈g₂⇒e∈g₃) = record
⊆-trans {MkGraph s₁ ns₁ es₁} {MkGraph s₂ ns₂ es₂} {MkGraph s₃ ns₃ es₃}
(Mk-⊆ n₁ p₁@refl g₁[]≡g₂[] e∈g₁⇒e∈g₂) (Mk-⊆ n₂ p₂@refl g₂[]≡g₃[] e∈g₂⇒e∈g₃) = record
{ n = n₁ +ⁿ n₂
; sg₂≡sg₁+n = +-assoc s₁ n₁ n₂
-- ; g₁[]≡g₂[] = λ idx → 1
-- lookup ns₁ idx ≡ lookup (cast p₁ ns₂) (idx ↑ˡ n) -- by g₁[]≡g₂[]
-- lookup (cast p₁ ns₂) (idx ↑ˡ n) ≡ lookup ns₂ (Fin.cast (sym p₁) (idx ↑ˡ n)) -- by lookup-cast₁
-- -------- s₁ + n₁ → s₂
-- ---------- Fin (s₁ + n₁)
-- ----------------------------- Fin s₂
-- lookup ns₂ (Fin.cast (sym p₁) (idx ↑ˡ n)) ≡ lookup (cast p₂ ns₃) ((Fin.cast (sym p₁) (idx ↑ˡ n₁) ↑ˡ n₂)) -- by g₂[]≡g₃[]
-- lookup (cast p₂ ns₃) ((Fin.cast (sym p₁) (idx ↑ˡ n₁) ↑ˡ n₂)) ≡ lookup ns₃ (Fin.cast (sym p₂) ((Fin.cast (sym p₁) (idx ↑ˡ n₁) ↑ˡ n₂))) -- by lookup-cast₂
-- -- ??
}
record Relaxable (T : Graph → Set) : Set where