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Proof step 1 from proof less-succ-leq (conclusion)

⊦ ⌜n⌝ < ⌜1⌝ + n∞ ↔ ¬ n∞ < ⌜n⌝

User applied rule structural induction

And closed the goal!

Rule argument

indvar: n∞

Additional information

Used simplifier rules: add-inf2: ⊦ ⌜m⌝ + ∞ = ∞;%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2;%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1;%less-inf2: ⊦ ⌜m⌝ < ∞;%less-inf1: ⊦ ¬ ∞ < n∞;%ls-natinf-to-nat-1-2: ⊦ ⌜n⌝ < ⌜m⌝ + ⌜n0⌝ ↔ n < m + n0;%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2;%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1;%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n;%natinf freely generated by ∞, ⌜ ⌝;;%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2