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Proof step 79 from proof inv-get-inverse (previous step)

leninv(nσ) = ⌜n0⌝ , n < n0, stutf(nσ) ⊦ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n) = ∞, nσ[max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n] = n

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 80:
max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n) = ⌜n1⌝ , leninv(nσ) = ⌜n0⌝ , n < n0, stutf(nσ) ⊦ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n) = ∞, nσ[n1] = n

Rule argument

spec: nat-inf-basic inst: name: elim seq: ⊦ n∞ ≠ ∞ → (n = n∞.n ↔ n∞ = ⌜n⌝ ) subst: [n∞, m] → [max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n), m] flags:

Additional information

Used simplifier rules: ⊦ n∞ ≠ ∞ → (n = n∞.n ↔ n∞ = ⌜n⌝ ); (elim) Used terms: max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n), m