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Proof step 1 from proof to-unwind-end (conclusion)

⌜n⌝ < # σ ⊦ σ to n + 1 = (σ to n) + ⌜σ[n] '⌝

User applied rule apply lemma

And obtained the following new goals

Proof step 2:
⊦ σ ≠ [] → (∃ a, σ0. σ = ⌜a '⌝ + σ0)
Proof step 3:
⌜n⌝ < # σ, σ ≠ [] → (∃ a, σ0. σ = ⌜a '⌝ + σ0) ⊦ σ to n + 1 = (σ to n) + ⌜σ[n] '⌝

Rule argument

spec: <toplevel> name: expand-cons seq: ⊦ σ ≠ [] → (∃ a, σ0. σ = ⌜a '⌝ + σ0) subst: [σ] → [σ]

Additional information

Used terms: σ