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Proof step 2 from proof elim-hd-tl (previous step)

⊦ a = hd(σ) ∧ σ0 = tl(σ) ↔ σ = a + σ0, σ = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ σ = ⌜hd(σ) '⌝ + tl(σ), σ = []

Rule argument

Additional information

Used simplifier rules: cons-append: ⊦ a + σ = ⌜a '⌝ + σ;%hd-lem: ⊦ hd(⌜a '⌝ + σ) = a;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%tl-lem: ⊦ tl(⌜a '⌝ + σ) = σ;