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Proof step 134 from proof inv-ls-succ (previous step)

nσ[n0] = n + 1, leninv(nσ) = ⌜n1⌝ , n + 1 < n1, n0 ≤ ((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to n1)[n], 1 + n < n1, stutf(nσ), ⌜n0⌝ < # nσ, (∀ n0. ∃ n1. n0 < n1 ∧ ⌜n1⌝ < # nσ ∧ nσ[n1] = n) ∨ (∀ n2. ¬ ⌜n2⌝ < # nσ ∨ nσ[n2] ≠ n), ∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = n + 1 → ¬ n0 < m ⊦

User applied rule case distinction

And obtained the following new goals

Proof step 135:
∀ n0. ∃ n1. n0 < n1 ∧ ⌜n1⌝ < # nσ ∧ nσ[n1] = n, nσ[n0] = n + 1, leninv(nσ) = ⌜n1⌝ , n + 1 < n1, n0 ≤ ((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to n1)[n], 1 + n < n1, stutf(nσ), ⌜n0⌝ < # nσ, ∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = n + 1 → ¬ n0 < m ⊦
Proof step 139:
∀ n2. ¬ ⌜n2⌝ < # nσ ∨ nσ[n2] ≠ n, nσ[n0] = n + 1, leninv(nσ) = ⌜n1⌝ , n + 1 < n1, n0 ≤ ((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to n1)[n], 1 + n < n1, stutf(nσ), ⌜n0⌝ < # nσ, ∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = n + 1 → ¬ n0 < m ⊦

Rule argument

pos: left 8

Proof step 134 from proof inv-ls-succ (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information