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Proof step 2 from proof toinftoinf-append-add (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 3:
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;%appendend-equal: ⊦ σ + σ0 = σ ↔ ¬ ¬(σ0 = [] ∨ # σ = ∞);%toinf-empty2: ⊦ ¬ # σ < n∞ → (σ to∞ n∞ = [] ↔ n∞ = ⌜0⌝ );%natinf freely generated by ∞, ⌜ ⌝;;%add-all-inf: ⊦ n∞ + ∞ = ∞; from specification nat-inf%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%inf-less: ⊦ n∞ < ∞ ↔ n∞ ≠ ∞; from specification nat-inf