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Proof step 1 from proof append-cancel-r-04 (conclusion)

⊦ finp(σ) → (⌜z⌝ = σ + ⌜z⌝ ↔ σ = [])

User applied rule structural induction

And closed the goal!

Rule argument

indvar: σ

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: ⊦ ⌜[]⌝ = [];%fin-empty: ⊦ ⌜x⌝ = [] ↔ x = [];%empty-append: ⊦ [] + σ = σ;%append-inf: ⊦ ⌜nf⌝ + σ = ⌜nf⌝ ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%fun-nonempty: ⊦ [] ≠ ⌜nf⌝ ;%stream freely generated by ⌜ ⌝, ⌜ ⌝;;%disj: ⊦ ⌜x⌝ ≠ ⌜nf⌝ ; from specification stream-basic%app-05: ⊦ x = y + x ↔ y = []; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%inj-02: ⊦ ⌜x⌝ = ⌜x0⌝ ↔ x = x0; from specification stream-basic