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Proof step 3 from proof toinftoinf-append-add (previous step)

⊦ (σ to∞ n∞) + σ0 to∞ n∞1 + n∞ = (σ to∞ n∞) + (σ0 to∞ n∞1), # σ < n∞, # σ0 < n∞1

User applied rule constructor cut

And obtained the following new goals

Proof step 4:
n∞ = ⌜m⌝ ⊦ (σ to∞ n∞) + σ0 to∞ n∞1 + n∞ = (σ to∞ n∞) + (σ0 to∞ n∞1), # σ0 < n∞1, # σ < n∞

Rule argument

var: n∞

Additional information

Used simplifier rules: toinf-inf: ⊦ σ to∞ ∞ = σ;%append-toinf-ls: ⊦ ¬ # σ < n∞ → σ + σ0 to∞ n∞ = σ to∞ n∞;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%append-cancel-l-02: ⊦ σ0 + σ = σ0 ↔ σ = [] ∨ ¬ finp(σ0);%toinf-empty2: ⊦ ¬ # σ < n∞ → (σ to∞ n∞ = [] ↔ n∞ = ⌜0⌝ );%size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ;%natinf freely generated by ∞, ⌜ ⌝;;% ⊦ n∞ + ∞ = ∞; (s)%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf% ⊦ n∞ < ∞ ↔ n∞ ≠ ∞; (s)%stream-fin-forward: ⊦ finp(σ) → (∃ x. ⌜x⌝ = σ); (forward) from specification stream-basic% ⊦ ⌜m⌝ ≠ ∞; (s)