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Proof step 57 from proof inv-ls-succ (previous step)

∞.n ≤ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n, n < nσ[m], ⌜m⌝ < # nσ, stutf(nσ), ∀ m2. (∃ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = m2 - 1 ∧ (# nσ ≠ ∞ ∨ ¬(∀ m1. m0 < m1 → nσ[m1] = m2 - 1))) → ¬ nσ[m] + 1 < m2, # nσ ≠ ∞ ∨ ¬(m < m0 → nσ[m0] = nσ[m]), (∀ n0. ∃ n1. n0 < n1 ∧ ⌜n1⌝ < # nσ ∧ nσ[n1] = n + 1) ∨ (∀ n0. ¬ ⌜n0⌝ < # nσ ∨ nσ[n0] ≠ n + 1) ⊦

User applied rule case distinction

And obtained the following new goals

Proof step 58:
∀ n0. ∃ n1. n0 < n1 ∧ ⌜n1⌝ < # nσ ∧ nσ[n1] = n + 1, ∞.n ≤ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n, n < nσ[m], ⌜m⌝ < # nσ, stutf(nσ), ∀ m2. (∃ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = m2 - 1 ∧ (# nσ ≠ ∞ ∨ ¬(∀ m1. m0 < m1 → nσ[m1] = m2 - 1))) → ¬ nσ[m] + 1 < m2, # nσ ≠ ∞ ∨ ¬(m < m0 → nσ[m0] = nσ[m]) ⊦
Proof step 81:
∀ n0. ¬ ⌜n0⌝ < # nσ ∨ nσ[n0] ≠ n + 1, ∞.n ≤ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n, n < nσ[m], ⌜m⌝ < # nσ, stutf(nσ), ∀ m2. (∃ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = m2 - 1 ∧ (# nσ ≠ ∞ ∨ ¬(∀ m1. m0 < m1 → nσ[m1] = m2 - 1))) → ¬ nσ[m] + 1 < m2, # nσ ≠ ∞ ∨ ¬(m < m0 → nσ[m0] = nσ[m]) ⊦

Rule argument

pos: left 7

Proof step 57 from proof inv-ls-succ (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information