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Proof step 176 from proof inv-get-inverse-between (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 177:
# nσ = ⌜m0⌝ + ⌜1⌝ , nσ[m1] = nσ[n1] + 1, nσ[n1] < nσ[m0], n1 + m + 1 < ∞.n, stutf(nσ), nσ[m1] ≤ nσ[m0], m1 ≤ m0, n1 ≤ m0, ∀ m. ¬ m0 < m ∧ nσ[m] = nσ[n1] → ¬ n1 < m, ∀ n. ∃ n0. n < n0 ∧ ¬ m0 < n0 ∧ nσ[n0] = nσ[m1] ⊦ nσ[n1 + m + 1] = nσ[m1]
Proof step 178:
# nσ = ⌜m0⌝ + ⌜1⌝ , nσ[m1] = nσ[n1] + 1, nσ[n1] < nσ[m0], n1 + m + 1 < ∞.n, stutf(nσ), nσ[m1] ≤ nσ[m0], m1 ≤ m0, n1 ≤ m0, ∀ m. ¬ m0 < m ∧ nσ[m] = nσ[n1] → ¬ n1 < m, ∀ n. m0 < n ∨ nσ[n] ≠ nσ[m1] ⊦ nσ[n1 + m + 1] = nσ[m1]

Rule argument

pos: left 10

Proof step 176 from proof inv-get-inverse-between (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information