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Proof step 4 from proof elim-hd-tl (previous step)

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

User applied rule structural induction

And closed the goal!

Rule argument

indvar: x

Additional information

Used simplifier rules: append-finfin: ⊦ ⌜x + y⌝ = ⌜x⌝ + ⌜y⌝ ;%hd-fin-lem: ⊦ hd(⌜a '⌝ + ⌜x⌝ ) = a;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%tl-fin-lem: ⊦ tl(⌜a '⌝ + ⌜x⌝ ) = ⌜x⌝ ;%eq-stream-to-list-2-2: ⊦ ⌜x⌝ + ⌜y⌝ = ⌜x0⌝ + ⌜z⌝ ↔ x + y = x0 + z;%list freely generated by [], +;;%c: ⊦ a + x = a ' + x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list