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Proof step 10 from proof append-split (previous step)

⌜x⌝ + ⌜nf0⌝ = ⌜x0⌝ + ⌜nf⌝ , # x = # x0 ⊦ x = x0 ∧ nf0 = nf

User applied rule structural induction

And obtained the following new goals

Proof step 11:
∀ nf0, x0, nf. ⌜x1⌝ + ⌜nf0⌝ = ⌜x0⌝ + ⌜nf⌝ ∧ # x1 = # x0 → x1 = x0 ∧ nf0 = nf, ⌜a + x1⌝ + ⌜nf0⌝ = ⌜x0⌝ + ⌜nf⌝ , #(a + x1) = # x0 ⊦ a + x1 = x0 ∧ nf0 = nf

Rule argument

indvar: x

Additional information

Used simplifier rules: empty: ⊦ ⌜[]⌝ = [];%empty-append: ⊦ [] + σ = σ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%list freely generated by [], +;;%size-01: ⊦ # [] = 0; from specification list-data%l: ⊦ # x = 0 ↔ x = []; from specification list-data%inj-01: ⊦ ⌜nf⌝ = ⌜nf0⌝ ↔ nf = nf0; from specification stream-basic