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Proof step 39 from proof leninv-succ (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 40:
# nσ = ∞, nσ[m] = nσ[m1], nσ[m1 + 1] = nσ[m0], nσ[m0] = nσ[m1] + 1, nσ[m2] = m3 + 1, nσ[m0] < nσ[m2], m < m2, m1 < m2, m1 < m0, m < m0, stutf(nσ), m ≤ m1 ⊦ nσ[m2] = nσ[m0], nσ[m2] = 0, ∃ m1. nσ[m1] = m3 ∧ ¬(∀ m. m1 < m → nσ[m] = m3)

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [nσ[m2], m3]

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: nσ[m2], m3