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Proof step 83 from proof inv-get-inverse-between (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 84:
leninv(nσ) = ⌜n0⌝ , n0 = n1 +1, 1 + n < n0, max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n + m + 1 < max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n + 1).n, stutf(nσ) ⊦ nσ[max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n + m + 1] = n + 1

Rule argument

var: n0

Additional information

Used simplifier rules: nat freely generated by 0, +1;;%n0 < n ⊦ ¬ m + (* n) < (* n0); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic