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Proof step 72 from proof inv-inverts-leq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 73:
# nσ = ⌜m⌝ + ⌜1⌝ , max∞(λ n0. ¬ m < n0 ∧ nσ[n0] = nσ[n]) = ⌜n1⌝ , n1 < m, stutf(nσ), n1 < n, nσ[n] ≤ nσ[m], n1 ≤ m, n ≤ m ⊦

Rule argument

Additional information

Used simplifier rules: disj: ⊦ ⌜m⌝ ≠ ∞; from specification nat-inf-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat