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Proof step 5 from proof elim-hd-tl (previous step)

⊦ ⌜nf⌝ = ⌜hd(⌜nf⌝ ) '⌝ + tl(⌜nf⌝ ), ⌜nf⌝ = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ ⌜nf⌝ = ⌜nf(0) '⌝ + ⌜λ n. nf(n + 1)⌝

Rule argument

Additional information

Used simplifier rules: hd-inf: ⊦ hd(⌜nf⌝ ) = nf(0);%tl-inf: ⊦ tl(⌜nf⌝ ) = ⌜λ n. nf(n +1)⌝ ;%fun-nonempty: ⊦ [] ≠ ⌜nf⌝ ;%succ: ⊦ m +1 = m + 1; from specification nat-basic2