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Proof step 4 from proof append-cancel-l-02 (previous step)

⊦ σ0 + ⌜x⌝ = σ0 ↔ x = [] ∨ ¬ finp(σ0)

User applied rule structural induction

And closed the goal!

Rule argument

indvar: σ0

Additional information

Used simplifier rules: eq-stream-to-list-2-1: ⊦ ⌜x⌝ + ⌜y⌝ = ⌜z⌝ ↔ x + y = z;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%empty: ⊦ ⌜[]⌝ = [];%append-empty: ⊦ σ + [] = σ;%append-inf: ⊦ ⌜nf⌝ + σ = ⌜nf⌝ ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%stream freely generated by ⌜ ⌝, ⌜ ⌝;;%inj-01: ⊦ ⌜nf⌝ = ⌜nf0⌝ ↔ nf = nf0; from specification stream-basic%test-01: ⊦ ¬ finp(⌜nf⌝ ); from specification stream-basic%app-04: ⊦ x = x + y ↔ y = []; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%test-02: ⊦ finp(⌜x⌝ ); from specification stream-basic%inj-02: ⊦ ⌜x⌝ = ⌜x0⌝ ↔ x = x0; from specification stream-basic