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Proof step 125 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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 126:
⊦ max∞(np) = ⌜n⌝ ↔ np(n) ∧ (∀ m. np(m) → ¬ n < m)
Proof step 127:
# nσ = ∞, nσ[n] = nσ[n1] + 1, n1 + m + 1 < n, nσ[n1] < nσ[m1], stutf(nσ), ∀ m. nσ[m] = nσ[n1] → ¬ n1 < m, ∀ m0. m1 < m0 → nσ[m0] = nσ[m1] + 1, ∀ m. nσ[m] = nσ[n1] + 1 → ¬ n < m ⊦ nσ[n1 + m + 1] = nσ[n1] + 1

Rule argument

spec: <toplevel> name: maxinf-fin seq: ⊦ max∞(np) = ⌜n⌝ ↔ np(n) ∧ (∀ m. np(m) → ¬ n < m) subst: [n, np] → [n, λ n0. nσ[n0] = nσ[n1] + 1] flags: <all paths>

Additional information

Used terms: n, λ n0. nσ[n0] = nσ[n1] + 1