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Proof step 11 from proof monls-notsmall (previous step)

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

User applied rule all left

And closed the goal!

Rule argument

pos: left 4 terms: n0 + 1 abort: F discard: F computed: F

Additional information

Used simplifier rules: add-fin: ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; from specification nat-inf%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%num-add: ⊦ ⌜(* n)⌝ + ⌜(* m)⌝ = ⌜n + m⌝ ; 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%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat Used terms: n0 + 1