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Proof step 14 from proof monls-exists-maxleq (previous step)

nσ[0] + 1 < nσ[m], nσ[0] < n, ⌜m⌝ < # nσ, nσ[0] < nσ[m], n < nσ[m], mon<(nσ), ∃ m0. nσ[m0] ≤ n ∧ n < nσ[m0 + 1] ∧ m0 ≤ 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 15:
nσ[0] < nσ[m0 + 1], nσ[m0] < nσ[m], nσ[m0] < nσ[m0 + 1], nσ[0] + 1 < nσ[m], nσ[0] < n, ⌜m⌝ < # nσ, nσ[0] < nσ[m], n < nσ[m], n < nσ[m0 + 1], nσ[0] + 1 < nσ[m0 + 1], mon<(nσ), m0 ≤ m, nσ[m0] ≤ n ⊦ 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)% ⊦ m < n → n ≠ 0; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic