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Proof step 160 from proof inv-get-inverse-between (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 161:
# nσ = ⌜m0⌝ + ⌜1⌝ , nσ[m1] < nσ[m0], ∞.n + m + 1 < max∞(λ n0. ¬ m0 < n0 ∧ nσ[n0] = nσ[m1] + 1).n, stutf(nσ), m1 ≤ m0, ∀ n0. ∃ n1. n0 < n1 ∧ ¬ m0 < n1 ∧ nσ[n1] = nσ[m1] ⊦ nσ[∞.n + m + 1] = nσ[m1] + 1
Proof step 162:
# nσ = ⌜m0⌝ + ⌜1⌝ , nσ[m1] < nσ[m0], ∞.n + m + 1 < max∞(λ n0. ¬ m0 < n0 ∧ nσ[n0] = nσ[m1] + 1).n, stutf(nσ), m1 ≤ m0, ∀ n0. m0 < n0 ∨ nσ[n0] ≠ nσ[m1] ⊦ nσ[∞.n + m + 1] = nσ[m1] + 1

Rule argument

pos: left 6

Proof step 160 from proof inv-get-inverse-between (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information