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Proof step 124 from proof inv-get-inverse-between (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 125:
# nσ = ∞, max∞(λ n0. nσ[n0] = nσ[n1] + 1) = ⌜n⌝ , nσ[n1] < nσ[m1], n1 + m + 1 < n, stutf(nσ), ∀ m0. m1 < m0 → nσ[m0] = nσ[m1] + 1, ∀ m. nσ[m] = nσ[n1] → ¬ n1 < m ⊦ nσ[n1 + m + 1] = nσ[n1] + 1

Rule argument

Additional information

Used simplifier rules: ⊦ ⌜m⌝ ≠ ∞; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic