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@ -704,11 +704,14 @@ The proof is by induction on the term `M`.
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The last lemma needed to prove `sub-sub` states that the `exts`
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function distributes with sequencing. It is a corollary of
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`commute-subst-rename`. We describe the proof below.
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`commute-subst-rename` as described below. (It would have been nicer
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to prove this directly by equational reasoning in the σ algebra, but
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that would require the `sub-assoc` equation, whose proof depends on
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`sub-sub`, which in turn depends on this lemma.)
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\begin{code}
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exts-seq : ∀{Γ Δ Δ′} {σ₁ : Subst Γ Δ} {σ₂ : Subst Δ Δ′}
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→ ∀ {A} → (exts σ₁ ⨟ exts σ₂) {A} ≡ exts (σ₁ ⨟ σ₂)
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→ ∀ {A} → (exts σ₁ ⨟ exts σ₂) {A} ≡ exts (σ₁ ⨟ σ₂)
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exts-seq = extensionality λ x → lemma {x = x}
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where
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lemma : ∀{Γ Δ Δ′}{A}{x : Γ , ★ ∋ A} {σ₁ : Subst Γ Δ}{σ₂ : Subst Δ Δ′}
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