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Proof step 1 from proof size-succ (conclusion)

⊦ # σ < ⌜n⌝ + ⌜1⌝ ↔ ¬ ⌜n⌝ < # σ

User applied rule structural induction

And closed the goal!

Rule argument

indvar: σ

Additional information

Used simplifier rules: size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ;%size-inf: ⊦ # ⌜nf⌝ = ∞;%stream freely generated by ⌜ ⌝, ⌜ ⌝;;%less-inf1: ⊦ ¬ ∞ < n∞; from specification nat-inf%less-inf2: ⊦ ⌜m⌝ < ∞; from specification nat-inf%less-succ-leq: ⊦ ⌜n⌝ < ⌜1⌝ + n∞ ↔ ¬ n∞ < ⌜n⌝ ; from specification nat-inf%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < 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