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Proof step 8 from proof mininv-inverts-inner (previous step)

# nσ = ⌜n0⌝ , min(nσ, nσ[n]) = n0, nσ[min(nσ, nσ[n]) - 1] < nσ[n], ⌜n⌝ < # nσ, mon<(nσ) ⊦ min(nσ, nσ[n]) = n, nσ = [], # nσ = ∞, nσ[n] = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
# nσ = ⌜min(nσ, nσ[n])⌝ , nσ[min(nσ, nσ[n]) - 1] < nσ[n], mon<(nσ), n < min(nσ, nσ[n]) ⊦ nσ[n] = 0, nσ = [], min(nσ, nσ[n]) = n, min(nσ, nσ[n]) = 0

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%disj: ⊦ ⌜m⌝ ≠ ∞; from specification nat-inf-basic