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Proof step 16 from proof lsleninv-1 (previous step)

stutf(nσ) ∧ ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → (∃ m0. m0 ≤ m ∧ nσ[m0] = n), m1 < nσ[m], m1 < n, n < nσ[m], ⌜m⌝ < # nσ, stutf(nσ), m1 + 1 < nσ[m], (# 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 17:
m1 < nσ[m], ⌜m⌝ < # nσ, stutf(nσ), m1 + 1 < nσ[m], m0 ≤ m, m1 < nσ[m0], nσ[m0] < nσ[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: f: ⊦ m < n → n ≠ 0; from specification nat-basic1%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic1%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic1%lels-03: ⊦ m < n → m ≤ n; from specification nat