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Proof step 30 from proof leninv-succ (previous step)

∃ m1. m ≤ m1 ∧ m1 < m0 ∧ nσ[m] = nσ[m1] ∧ nσ[m1 + 1] = nσ[m1] + 1, # nσ = ∞, nσ[m0] = nσ[m] + 1, m < m0, stutf(nσ), ∀ m0. (m0 ≠ 0 → (∃ m1. nσ[m1] = m0 - 1 ∧ ¬(∀ m2. m1 < m2 → nσ[m2] = m0 - 1))) → ¬ nσ[m] + 1 < m0 ⊦ m0 = 0, ∃ m0. nσ[m0] = nσ[m] ∧ (∀ m1. m0 < m1 → nσ[m1] = nσ[m0] + 1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
nσ[m0] = nσ[m1] + 1, # nσ = ∞, nσ[m1 + 1] = nσ[m0], nσ[m] = nσ[m1], m < m0, stutf(nσ), m1 < m0, m ≤ m1, ∀ m0. (m0 ≠ 0 → (∃ m1. nσ[m1] = m0 - 1 ∧ ¬(∀ m2. m1 < m2 → nσ[m2] = m0 - 1))) → ¬ nσ[m1] + 1 < m0 ⊦ m0 = 0, ∃ m0. nσ[m0] = nσ[m1] ∧ (∀ m1. m0 < m1 → nσ[m1] = nσ[m0] + 1)

Rule argument

Additional information

Used simplifier rules: fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat