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Proof step 62 from proof leninv-succ (previous step)

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

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

pos: right 3 terms: m2

Additional information

Used simplifier rules: lels-03: ⊦ m < n → m ≤ n; from specification nat%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat Used terms: m2