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Nov 13th, 2019
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  1. Theorem “Initialisation for `rev`”:
  2. true ⇒⁅ xs := xs₀ ⨾ ys := 𝜖 ⁆ reverse xs ⌢ ys = reverse xs₀
  3. Proof:
  4. reverse xs ⌢ ys = reverse xs₀
  5. ⁅ ys := 𝜖 ⁆⇐ ⟨ “Assignment” with substitution ⟩
  6. reverse xs ⌢ 𝜖 = reverse xs₀
  7. ⁅ xs := xs₀ ⁆⇐ ⟨ “Assignment” with substitution ⟩
  8. reverse xs₀ ⌢ 𝜖 = reverse xs₀
  9. ≡⟨“Right-identity of ⌢”⟩
  10. reverse xs₀ = reverse xs₀
  11. ≡⟨“Reflexivity of =”⟩
  12. true
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