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Proof step 57 from proof inv-get-inverse-last (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 58:
nσ[m1 + 1] = nσ[m1] + 1, # nσ = ∞, stutf(nσ), ∀ m0. m1 < m0 → nσ[m0] = nσ[m1] + 1, ∀ m0. nσ[m0] = nσ[m1] → ¬ m1 < m0 ⊦ nσ[m1 + m + 1] = nσ[m1] + 1

Rule argument

Additional information

Used simplifier rules: ler: ⊦ m ≤ m; from specification nat%anti: ⊦ m ≤ n → (n ≤ m ↔ m = n); from specification nat%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat