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Proof step 50 from proof inv-inverts (previous step)

nσ[n + 1] = nσ[n] + 1, ⌜n⌝ + ⌜1⌝ < # nσ, stutf(nσ) ⊦ (leninv(nσ) = ∞ ⊃ ⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ ;⌜(λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to leninv(nσ).n⌝ ) [nσ[n] ] = n, max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) = ⌜n⌝ , max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) = ∞

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 51:
⊦ n∞ = ∞ ↔ ¬(∃ n. n∞ = ⌜n⌝ )
Proof step 52:
nσ[n + 1] = nσ[n] + 1, ⌜n⌝ + ⌜1⌝ < # nσ, stutf(nσ) ⊦ (leninv(nσ) = ∞ ⊃ ⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ ;⌜(λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to leninv(nσ).n⌝ ) [nσ[n] ] = n, max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) = ⌜n⌝ , ∀ n0. max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) ≠ ⌜n0⌝

Rule argument

spec: nat-inf name: notinf-fin seq: ⊦ n∞ = ∞ ↔ ¬(∃ n. n∞ = ⌜n⌝ ) subst: [n∞] → [max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n])] flags: <all paths>

Additional information

Used terms: max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n])