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Proof step 59 from proof inv-get-inverse-succ (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 60:
leninv(nσ) = ⌜n0⌝ , n0 = n1 +1, ⌜max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n⌝ + ⌜1⌝ < # nσ, n < n0, stutf(nσ) ⊦ nσ[max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n + 1] = n + 1

Rule argument

var: n0

Additional information

Used simplifier rules: nat freely generated by 0, +1;;% ⊦ ¬ m < 0; (s)