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Proof step 107 from proof inv-get-inverse-between (previous step)

# nσ = ∞, max∞(λ n0. nσ[n0] = n) = ⌜n1⌝ , n1 + m + 1 < max∞(λ n0. nσ[n0] = n + 1).n, n < nσ[m1], stutf(nσ), ∀ m0. m1 < m0 → nσ[m0] = nσ[m1] + 1 ⊦ max∞(λ n0. nσ[n0] = n + 1).n = 0, nσ[n1 + m + 1] = n + 1, nσ[m1] = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 108:
⊦ max∞(np) = ⌜n⌝ ↔ np(n) ∧ (∀ m. np(m) → ¬ n < m)
Proof step 109:
# nσ = ∞, nσ[n1] = n ∧ (∀ m. nσ[m] = n → ¬ n1 < m), n1 + m + 1 < max∞(λ n0. nσ[n0] = n + 1).n, n < nσ[m1], stutf(nσ), ∀ m0. m1 < m0 → nσ[m0] = nσ[m1] + 1 ⊦ max∞(λ n0. nσ[n0] = n + 1).n = 0, nσ[n1 + m + 1] = n + 1, nσ[m1] = 0

Rule argument

spec: inst: name: maxinf-fin seq: ⊦ max∞(np) = ⌜n⌝ ↔ np(n) ∧ (∀ m. np(m) → ¬ n < m) subst: [n, np] → [n1, λ n0. nσ[n0] = n] flags: rewrite, current

Additional information

Used terms: n1, λ n0. nσ[n0] = n