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Proof step 69 from proof leninv-succ (previous step)

nσ[0] = 0, # nσ = ∞, nσ[(m1 + 1) + m] = nσ[m] + 1, nσ[m + 1] = nσ[m] ∨ nσ[m + 1] = nσ[m] + 1 ⊦ nσ = [], nσ[m] = nσ[m + 1], ∃ m0. m ≤ m0 ∧ ¬ m1 + m < m0 ∧ nσ[m] = nσ[m0] ∧ nσ[m0 + 1] = nσ[m0] + 1, nσ[m1 + m] = nσ[m] + 1 ∧ m1 ≠ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 70:
nσ[m + 1] = nσ[m] + 1, nσ[(m1 + 1) + m] = nσ[m] + 1, # nσ = ∞, nσ[0] = 0 ⊦ nσ = [], nσ[m1 + m] = nσ[m] + 1 ∧ m1 ≠ 0, ∃ m0. m ≤ m0 ∧ ¬ m1 + m < m0 ∧ nσ[m] = nσ[m0] ∧ nσ[m0 + 1] = nσ[m0] + 1

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%eq: ⊦ m = m + n ↔ n = 0; from specification nat-basic2