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Proof step 132 from proof inv-get-inverse-between (previous step)

nσ[n] = nσ[n1] + 1, # nσ = ∞, nσ[n] ≤ nσ[m1], n1 + m + 1 < n, nσ[n1] < nσ[m1], stutf(nσ), n ≤ m1, n1 + m + 1 < m1, n1 < m1, ∀ m. nσ[m] = nσ[n] → ¬ n < m, ∀ m. nσ[m] = nσ[n1] → ¬ n1 < m, ∀ m0. m1 < m0 → nσ[m0] = nσ[m1] + 1 ⊦ m1 = 0, n = 0, nσ[n1 + m + 1] = nσ[n], nσ[m1] = 0, nσ[n] = nσ[m1] + 1

User applied rule all left

And obtained the following new goals

Proof step 133:
nσ[n] = nσ[n1] + 1, # nσ = ∞, nσ[n] ≤ nσ[m1], n1 + m + 1 < n, nσ[n1] < nσ[m1], stutf(nσ), n ≤ m1, n1 + m + 1 < m1, n1 < m1, ∀ m. nσ[m] = nσ[n] → ¬ n < m, nσ[n1 + 1] = nσ[n1] → ¬ n1 < n1 + 1, ∀ m. nσ[m] = nσ[n1] → ¬ n1 < m, ∀ m0. m1 < m0 → nσ[m0] = nσ[m1] + 1 ⊦ m1 = 0, n = 0, nσ[n1 + m + 1] = nσ[n], nσ[m1] = 0, nσ[n] = nσ[m1] + 1

Rule argument

pos: left 11 terms: n1 + 1 abort: F discard: F computed: T

Additional information

Used terms: n1 + 1