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Proof step 12 from proof inv-inverts (previous step)

nσ[n + 1] = nσ[n] + 1, leninv(nσ) = ⌜n1⌝ , max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) = ⌜n⌝ , n1 = 0, ⌜n⌝ + ⌜1⌝ < # nσ, stutf(nσ) ⊦ ((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to n1)[nσ[n]] = n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
nσ[n + 1] = nσ[n] + 1, leninv(nσ) = ⌜0⌝ , max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) = ⌜n⌝ , ⌜n⌝ + ⌜1⌝ < # nσ, stutf(nσ) ⊦ ([])[nσ[n]] = n

Rule argument

Additional information

Used simplifier rules: ⊦ nnf to 0 = []; (s)