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- Theorem “Initialisation for `rev`”:
- true ⇒⁅ xs := xs₀ ⨾ ys := 𝜖 ⁆ reverse xs ⌢ ys = reverse xs₀
- Proof:
- reverse xs ⌢ ys = reverse xs₀
- ⁅ ys := 𝜖 ⁆⇐ ⟨ “Assignment” with substitution ⟩
- reverse xs ⌢ 𝜖 = reverse xs₀
- ⁅ xs := xs₀ ⁆⇐ ⟨ “Assignment” with substitution ⟩
- reverse xs₀ ⌢ 𝜖 = reverse xs₀
- ≡⟨“Right-identity of ⌢”⟩
- reverse xs₀ = reverse xs₀
- ≡⟨“Reflexivity of =”⟩
- true
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