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Proof step 8 from proof monls-exists-maxleq (previous step)

⌜m1⌝ + ⌜1⌝ < # nσ, nσ[0] < nσ[m1 + 1], mon<(nσ) ⊦ nσ[m1] < nσ[m1 + 1] ∧ nσ[m1 + 1] ≤ nσ[m1 + 1] ∧ m1 ≤ m1 + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
nσ[0] < nσ[m1 + 1], ⌜m1⌝ + ⌜1⌝ < # nσ, nσ[0] < nσ[m1], mon<(nσ), nσ[m1 + 1] ≤ nσ[m1] ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m + n; (s)% ⊦ m ≤ m; (s)