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Proof step 3 from proof append-extract-list (previous step)

⊦ (⌜x⌝ + ⌜x0⌝ ).l = x + x0

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 4:
∀ x0. (⌜x1⌝ + ⌜x0⌝ ).l = x1 + x0 ⊦ (⌜a + x1⌝ + ⌜x0⌝ ).l = (a + x1) + x0

Rule argument

term: x

Additional information

Used simplifier rules: empty: ⊦ ⌜[]⌝ = [];%empty-append: ⊦ [] + σ = σ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%list freely generated by [], +;;%sel-02: ⊦ ⌜x⌝ .l = x; from specification stream-basic%Nil: ⊦ [] + x = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list