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Proof step 12 from proof monls-notsmall (previous step)

nσ[0] = 0, ⌜2⌝ + ⌜n0⌝ < # nσ, ⌜n0⌝ + ⌜1⌝ < # nσ, n0 < nσ[n0 + 1], nσ[2 + n0] ≤ n0 + 1, nσ[2 + n0] ≤ nσ[n0 + 1], ∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1] ⊦

User applied rule all left

And closed the goal!

Rule argument

pos: left 7 terms: n0 + 1 abort: F discard: F computed: F

Additional information

Used simplifier rules: ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ⌜(* n)⌝ + ⌜(* m)⌝ = ⌜n + m⌝ ; (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% ⊦ m ≤ n → (n < m ↔ false); (s) Used terms: n0 + 1