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Proof step 18 from proof lsleninv-1 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
# nσ = ∞, nσ[m2] < nσ[m], nσ[m0] < nσ[m], nσ[m2] < nσ[m0], m0 ≤ m, stutf(nσ), nσ[m2] + 1 < nσ[m], ∀ m0. m2 < m0 → nσ[m0] = nσ[m2] + 1 ⊦

Rule argument

Additional information

Used simplifier rules: less-inf2: ⊦ ⌜m⌝ < ∞; from specification nat-inf%succ: ⊦ m +1 = m + 1; from specification nat-basic2%trans-1: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic1%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic1