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Proof step 2 from proof size-toinf (previous step)

⊦ #(σ to∞ n∞) = n∞, # σ < n∞

Heuristic structural induction applied rule structural induction

And closed the goal!

Rule argument

term: n∞

Additional information

Used simplifier rules: toinf-inf: ⊦ σ to∞ ∞ = σ;%toinf-fin: ⊦ σ to∞ ⌜n⌝ = σ to n;%size-to: ¬ # σ < ⌜n⌝ ⊦ #(σ to n) = ⌜n⌝ ;%natinf freely generated by ∞, ⌜ ⌝;;%inj: ⊦ ⌜m⌝ = ⌜m0⌝ ↔ m = m0; from specification nat-inf-basic%inf-less: ⊦ n∞ < ∞ ↔ n∞ ≠ ∞; from specification nat-inf