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Proof step 17 from proof lsleninv-1 (previous step)

m1 < nσ[m], ⌜m⌝ < # nσ, n < nσ[m], m1 < n, m1 + 1 < nσ[m], stutf(nσ), stutf(nσ) ∧ ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → (∃ m0. m0 ≤ m ∧ nσ[m0] = n), (# nσ = ∞ ⊃ nσ[m2] = m1 ∧ (∀ m0. m2 < m0 → nσ[m0] = nσ[m2] + 1);nσ[(# nσ).n - 1] = m1) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
m1 + 1 < nσ[m], ⌜m⌝ < # nσ, m1 < nσ[m], m1 < nσ[m0], nσ[m0] < nσ[m], stutf(nσ), m0 ≤ m, (# nσ = ∞ ⊃ nσ[m2] = m1 ∧ (∀ m0. m2 < m0 → nσ[m0] = nσ[m2] + 1);nσ[(# nσ).n - 1] = m1) ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m < n → m ≤ n; (s)