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Proof step 50 from proof leninv-succ (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 51:
∀ m0, m, nσ. m1 = m0 - m ∧ # nσ = ∞ ∧ nσ[m0] = nσ[m] + 1 ∧ m < m0 ∧ stutf(nσ) → (∃ m1. m ≤ m1 ∧ m1 < m0 ∧ nσ[m] = nσ[m1] ∧ nσ[m1 + 1] = nσ[m1] + 1), m1 +1 = m0 - m, # nσ = ∞, nσ[m0] = nσ[m] + 1, m < m0, stutf(nσ) ⊦ ∃ m1. m ≤ m1 ∧ m1 < m0 ∧ nσ[m] = nσ[m1] ∧ nσ[m1 + 1] = nσ[m1] + 1

Rule argument

term: m0 - m

Additional information

Used simplifier rules: nat freely generated by 0, +1;;%zero-01: ⊦ n < m → m - n ≠ 0; from specification nat