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Proof step 6 from proof mininv-inverts-inner (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
min(nσ, nσ[n]) = (# nσ).n, nσ[min(nσ, nσ[n]) - 1] < nσ[n], ⌜n⌝ < # nσ, mon<(nσ) ⊦ min(nσ, nσ[n]) = n, nσ = [], # nσ = ∞, nσ[n] = 0

Rule argument

Additional information

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