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Proof step 15 from proof monls-exists-maxleq (previous step)

nσ[0] < nσ[m0 + 1], nσ[m0] < nσ[m], nσ[m0] < nσ[m0 + 1], nσ[0] + 1 < nσ[m], nσ[0] < n, mon<(nσ), nσ[0] < nσ[m], ⌜m⌝ < # nσ, n < nσ[m], m0 ≤ m, n < nσ[m0 + 1], nσ[m0] ≤ n, nσ[0] + 1 < nσ[m0 + 1] ⊦ nσ[m0 + 1] = 0, n = nσ[m], n = 0, nσ[m] = 0, nσ[m0] < n ∧ n ≤ nσ[m0 + 1] ∧ m0 ≤ m, ∃ m0. nσ[m0] < n ∧ n ≤ nσ[m0 + 1] ∧ m0 ≤ m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
nσ[0] + 1 < nσ[m0 + 1], m0 ≤ m, ⌜m⌝ < # nσ, nσ[0] < nσ[m], mon<(nσ), nσ[0] < nσ[m0], nσ[0] + 1 < nσ[m], nσ[m0] < nσ[m0 + 1], nσ[m0] < nσ[m], nσ[0] < nσ[m0 + 1] ⊦ nσ[m] = 0, nσ[m0] = 0, nσ[m0 + 1] = 0, ∃ m1. nσ[m1] < nσ[m0] ∧ nσ[m0] ≤ nσ[m1 + 1] ∧ m1 ≤ m

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%ler: ⊦ m ≤ m; from specification nat%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic1%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic1%anti: ⊦ m ≤ n → (n ≤ m ↔ m = n); from specification nat%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%lels-03: ⊦ m < n → m ≤ n; from specification nat