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Proof step 45 from proof inv-inverts (previous step)

∃ n1. n + 1 < n1 ∧ ⌜n1⌝ < # nσ ∧ nσ[n1] = nσ[n], 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
nσ[n0] = nσ[n], nσ[n + 1] = nσ[n] + 1, n + 1 < n0, ⌜n0⌝ < # nσ, ⌜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, n0 = 0

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1