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Proof step 3 from proof append-cancel-l (previous step)

⌜x⌝ + ⌜x0⌝ = ⌜x⌝ + σ1 ⊦ ⌜x0⌝ = σ1

User applied rule structural induction

And closed the goal!

Rule argument

indvar: σ1

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 ⌜ ⌝, ⌜ ⌝;;%app-01: ⊦ x + y = x + z ↔ y = z; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list