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Proof step 16 from proof mininv-inverts-inner (previous step)

⌜min(nσ, nσ[n])⌝ < # nσ, nσ[n] ≤ nσ[min(nσ, nσ[n])], ⌜n⌝ < # nσ, mon<(nσ), min(nσ, nσ[n]) < n, ∀ m. ⌜m⌝ < # nσ ∧ nσ[n] ≤ nσ[m] → min(nσ, nσ[n]) ≤ m, # nσ = ∞ ∨ ¬ nσ[(# nσ).n - 1] < nσ[n] ⊦ min(nσ, nσ[n]) = n, nσ = [], n = 0

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: inst: name: monls-ls seq: ⊦ mon<(nσ) ∧ m < n ∧ ⌜n⌝ < # nσ → nσ[m] < nσ[n] subst: [nσ, m, n] → [nσ, min(nσ, nσ[n]), n] flags: current, []

Additional information

Used simplifier rules: mininv-inverts-weak: ⊦ mon<(nσ) ∧ ⌜min(nσ, n)⌝ < # nσ → (¬ ¬ nσ[min(nσ, n)] < n ↔ false); Used terms: nσ, min(nσ, nσ[n]), n