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Proof step 7 from proof mininv-inverts-inner-succ (previous step)

min(nσ, nσ[n] + 1) = (# nσ).n, ⌜n⌝ < # nσ, mon<(nσ) ⊦ # nσ = ∞, min(nσ, nσ[n] + 1) = n + 1, nσ = [], nσ[n] < nσ[(# nσ).n - 1]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
min(nσ, nσ[n] + 1) = (# nσ).n, ⌜n⌝ < # nσ, mon<(nσ), nσ[(# nσ).n - 1] ≤ nσ[n] ⊦ # nσ = ∞, (# nσ).n = n + 1, nσ = []

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)