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Proof step 63 from proof inv-ls-succ (previous step)

# nσ = ⌜n0⌝ , m < n0, stutf(nσ), ∞.n ≤ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n, n < nσ[m], ∀ m1. (∃ m0. m0 < n0 ∧ nσ[m0] = m1 - 1) → ¬ nσ[m] + 1 < m1, ∀ n0. ∃ n1. n0 < n1 ∧ ⌜n1⌝ < # nσ ∧ nσ[n1] = n + 1 ⊦

User applied rule all left

And closed the goal!

Rule argument

pos: left 7 terms: n0 abort: F discard: T computed: F

Additional information

Used simplifier rules: eqle-one: ⊦ m = n + 1 ∧ n < n0 → m ≤ n0; (forward) from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic1%trans-1: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic1%f: ⊦ m < n → n ≠ 0; from specification nat-basic1%succ: ⊦ m +1 = m + 1; from specification nat-basic2%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%ls-02: ⊦ m < n → ¬ n < m; from specification nat-basic1 Used terms: n0