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Proof step 86 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. ¬ ⌜n0⌝ < # nσ ∨ nσ[n0] ≠ n + 1 ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 87:
⊦ stutf(nσ) ∧ ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → (∃ m0. m0 ≤ m ∧ nσ[m0] = n)
Proof step 88:
stutf(nσ) ∧ ⌜m⌝ < # nσ ∧ n + 1 ≤ nσ[m] → (∃ m0. m0 ≤ m ∧ nσ[m0] = n + 1), # 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. ¬ ⌜n0⌝ < # nσ ∨ nσ[n0] ≠ n + 1 ⊦

Rule argument

spec: inst: name: stutf-alltaken seq: ⊦ stutf(nσ) ∧ ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → (∃ m0. m0 ≤ m ∧ nσ[m0] = n) subst: [nσ, m, n] → [nσ, m, n + 1] flags: current, []

Additional information

Used terms: nσ, m, n + 1