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Proof step 11 from proof monls-exists-maxleq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
n < nσ[m], nσ[0] < nσ[m], ⌜m⌝ < # nσ, nσ[0] < n, nσ[0] + 1 < nσ[m], mon<(nσ) ⊦ n = nσ[m], ∃ m0. nσ[m0] < n ∧ n ≤ nσ[m0 + 1] ∧ m0 ≤ m

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)