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Proof step 7 from proof append-split (previous step)

⌜x⌝ + σ0 = ⌜x0⌝ + ⌜x1⌝ , # x = # x0 ⊦ x = x0 ∧ σ0 = ⌜x1⌝

User applied rule structural induction

And closed the goal!

Rule argument

indvar: σ0

Additional information

Used simplifier rules: eq-stream-to-list-2-2: ⊦ ⌜x⌝ + ⌜y⌝ = ⌜x0⌝ + ⌜z⌝ ↔ x + y = x0 + z;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%neq-fin-inf-02: ⊦ σ0 + ⌜x⌝ = σ + ⌜nf0⌝ ↔ σ0 = σ + ⌜nf0⌝ ;%neq-fin-inf-01: ⊦ ⌜x⌝ ≠ σ + ⌜nf0⌝ ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%stream freely generated by ⌜ ⌝, ⌜ ⌝;;%len-01: ⊦ # x = # z → (x + y = z + y0 ↔ x = z ∧ y = y0); from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%inj-02: ⊦ ⌜x⌝ = ⌜x0⌝ ↔ x = x0; from specification stream-basic