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Proof step 6 from proof monls-notsmall (previous step)

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

User applied rule all left

And closed the goal!

Rule argument

pos: left 3 terms: 0 abort: F discard: T computed: F

Additional information

Used simplifier rules: ⊦ n∞ + ⌜0⌝ = n∞; (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% ⊦ ⌜1⌝ < n∞ ↔ n∞ ≠ ⌜0⌝ ∧ n∞ ≠ ⌜1⌝ ; (s)% ⊦ # nσ = ⌜0⌝ ↔ nσ = []; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n → n ≠ 0; (s) Used terms: 0