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Proof step 1 from proof append-cut1 (conclusion)

⊦ σ + σ1 = σ + σ2 ↔ σ1 = σ2 ∨ # σ = ∞

User applied rule structural induction

And closed the goal!

Rule argument

indvar: σ

Additional information

Used simplifier rules: append-cancel-l: ⊦ ⌜x⌝ + σ0 = ⌜x⌝ + σ1 ↔ σ0 = σ1;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ;%append-inf: ⊦ ⌜nf⌝ + σ = ⌜nf⌝ ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%size-inf: ⊦ # ⌜nf⌝ = ∞;%stream freely generated by ⌜ ⌝, ⌜ ⌝;;%inj-01: ⊦ ⌜nf⌝ = ⌜nf0⌝ ↔ nf = nf0; from specification stream-basic%disj: ⊦ ⌜m⌝ ≠ ∞; from specification nat-inf-basic