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Proof step 8 from proof mininv-stays-if-not-taken (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
nσ[min(nσ, n + 1) - 1] = n, min(nσ, n + 1) = (# nσ).n, ⌜min(nσ, n)⌝ < # nσ, mon<(nσ), n ≤ nσ[min(nσ, n)], ∀ m. ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → min(nσ, n) ≤ m, ∀ m. ⌜m⌝ < # nσ → nσ[m] ≠ n ⊦ # nσ = ∞, min(nσ, n + 1) = min(nσ, n), nσ = []

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)