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Proof step 9 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) ⊦ # nσ = ∞, min(nσ, nσ[n]) = n, nσ = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
# nσ = ⌜min(nσ, nσ[n])⌝ , n < min(nσ, nσ[n]), nσ[min(nσ, nσ[n]) - 1] < nσ[n], mon<(nσ) ⊦ min(nσ, nσ[n]) = n, nσ = []

Rule argument

Additional information

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