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Proof step 89 from proof inv-ls-succ (previous step)

# nσ = ⌜n0⌝ , nσ[m0] = n + 1, ∞.n ≤ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n, stutf(nσ), m < n0, m0 ≤ m, m0 < n0, n < nσ[m], ∀ n0. ¬ ⌜n0⌝ < # nσ ∨ nσ[n0] ≠ n + 1, ∀ m1. (∃ m0. m0 < n0 ∧ nσ[m0] = m1 - 1) → ¬ nσ[m] + 1 < m1 ⊦

User applied rule all left

And closed the goal!

Rule argument

pos: left 9 terms: m0 abort: F discard: T computed: T

Additional information

Used simplifier rules: less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat Used terms: m0