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Proof step 27 from proof min-stutters (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
⌜min(nσ, n)⌝ + ⌜1⌝ = # nσ, n < nσ[(# nσ).n - 1], ⌜min(nσ, n)⌝ < # nσ, n ≤ nσ[min(nσ, n)], mon<(nσ), n < nσ[min(nσ, n + 1)], ⌜min(nσ, n + 1)⌝ < # nσ, min(nσ, n) < min(nσ, n + 1), min(nσ, n) + 1 < min(nσ, n + 1), ∀ m. ⌜m⌝ < # nσ ∧ n < nσ[m] → min(nσ, n + 1) ≤ m, ∀ m. ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → min(nσ, n) ≤ m ⊦ nσ = [], min(nσ, n + 1) = min(nσ, n), min(nσ, n + 1) = 1 + min(nσ, n), n < nσ[min(nσ, n)]

Rule argument

Additional information

Used simplifier rules: ls-02: ⊦ m < n → ¬ n < m; from specification nat-basic1%lels-02: ⊦ m ≠ n → (m ≤ n ↔ m < n); from specification nat