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Proof step 14 from proof mininv-inverts-inner-succ (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
⌜n⌝ < # nσ, ⌜min(nσ, nσ[n] + 1)⌝ < # nσ, nσ[n] < nσ[min(nσ, nσ[n] + 1)], mon<(nσ), ∀ m. ⌜m⌝ < # nσ ∧ nσ[n] < nσ[m] → min(nσ, nσ[n] + 1) ≤ m, # nσ = ∞ ∨ nσ[n] < nσ[(# nσ).n - 1] ⊦ min(nσ, nσ[n] + 1) = n + 1, nσ = []

Rule argument

Additional information

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