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| author | Jacques Comeaux <jacquesrcomeaux@protonmail.com> | 2024-02-22 11:22:01 -0600 |
|---|---|---|
| committer | Jacques Comeaux <jacquesrcomeaux@protonmail.com> | 2024-02-22 11:22:01 -0600 |
| commit | d65d60fe31f0c25c7e845d66e37c47e4f22924e1 (patch) | |
| tree | 42d06990994e4ca34b42be5dd669b149d21ff67b /FinMerge/Properties.agda | |
| parent | 94a6a0f847a2a1c02347bead7901656e4bd33fdb (diff) | |
Fill in omitted proof
Diffstat (limited to 'FinMerge/Properties.agda')
| -rw-r--r-- | FinMerge/Properties.agda | 18 |
1 files changed, 17 insertions, 1 deletions
diff --git a/FinMerge/Properties.agda b/FinMerge/Properties.agda index 6d6c964..e403d99 100644 --- a/FinMerge/Properties.agda +++ b/FinMerge/Properties.agda @@ -111,7 +111,23 @@ glue-iter-append → (f g : Fin m → Fin y) → (h : Fin n → Fin y) → Σ[ h′ ∈ (Fin y → Fin (proj₁ (glue-iter f g h))) ] (proj₂ (glue-iter f g h) ≡ h′ ∘ h) -glue-iter-append f g h = ? +glue-iter-append {ℕ.zero} f g h = id , refl +glue-iter-append {ℕ.suc m} f g h with compare (f (# 0)) (g (# 0)) +glue-iter-append {ℕ.suc m} f g h | less (f0<g0 , s≤s g0≤n) + with + glue-iter-append + (merge (f0<g0 , g0≤n) ∘ f ∘ Fin.suc) + (merge (f0<g0 , g0≤n) ∘ g ∘ Fin.suc) + (merge (f0<g0 , g0≤n) ∘ h) +... | h′ , glue-p∘h≡h′∘p∘h = h′ ∘ merge (f0<g0 , g0≤n) , glue-p∘h≡h′∘p∘h +glue-iter-append {ℕ.suc m} f g h | equal x = glue-iter-append (f ∘ Fin.suc) (g ∘ Fin.suc) h +glue-iter-append {ℕ.suc m} f g h | greater (g0<f0 , s≤s f0≤n) + with + glue-iter-append + (merge (g0<f0 , f0≤n) ∘ f ∘ Fin.suc) + (merge (g0<f0 , f0≤n) ∘ g ∘ Fin.suc) + (merge (g0<f0 , f0≤n) ∘ h) +... | h′ , glue-p∘h≡h′∘p∘h = h′ ∘ merge (g0<f0 , f0≤n) , glue-p∘h≡h′∘p∘h lemma₂ : (f g : Fin (ℕ.suc m) → Fin n) |