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Proof step 10 from proof mininv-stays-if-not-taken (previous step)

# nσ = ⌜n0⌝ , nσ[min(nσ, n + 1) - 1] = n, min(nσ, n + 1) = n0, ⌜min(nσ, n)⌝ < # nσ, mon<(nσ), n ≤ nσ[min(nσ, n)], ∀ m. ⌜m⌝ < # nσ → nσ[m] ≠ n, ∀ m. ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → min(nσ, n) ≤ m ⊦ # nσ = ∞, min(nσ, n + 1) = min(nσ, n), nσ = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
# nσ = ⌜min(nσ, n + 1)⌝ , nσ[min(nσ, n + 1) - 1] = n, min(nσ, n) < min(nσ, n + 1), mon<(nσ), n ≤ nσ[min(nσ, n)], ∀ m. m < min(nσ, n + 1) ∧ n ≤ nσ[m] → min(nσ, n) ≤ m, ∀ m. m < min(nσ, nσ[m] + 1) → nσ[m] ≠ n ⊦ min(nσ, n + 1) = min(nσ, 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)