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Proof step 82 from proof leninv-succ (previous step)

m0 = m3 + 1, # nσ = ∞, nσ[m1] = m3, stutf(nσ), nσ[m] + 1 < m0, m1 < m2, ∀ m0. m < m0 → nσ[m0] = nσ[m] + 1 ⊦ m0 = 0, nσ[m2] = m3, m2 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 83:
# nσ = ∞, m1 < m2, stutf(nσ), nσ[m] < nσ[m1], ∀ m0. m < m0 → nσ[m0] = nσ[m] + 1 ⊦ nσ[m2] = nσ[m1], m2 = 0, nσ[m1] = 0

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%l: ⊦ m + n < m + n0 ↔ n < n0; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2