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Proof step 5 from proof numeral-10 (previous step)

(m * m0 + m) + n0 < m2 * m, m2 ≤ m0, ∀ m, n0, m2. m0 * m + n0 < m2 * m ∧ m2 < m0 → m = 0 ∨ m2 = 0 ⊦ m = 0, m2 = 0

User applied rule structural induction

And obtained the following new goals

Proof step 6:
(m * m0 + m) + n0 < m1 +1 * m, m1 +1 ≤ m0, ∀ m, n0, m2. m0 * m + n0 < m2 * m ∧ m2 < m0 → m = 0 ∨ m2 = 0, ∀ m, m0, n0. (m * m0 + m) + n0 < m1 * m ∧ m1 ≤ m0 ∧ (∀ m, n0, m2. m0 * m + n0 < m2 * m ∧ m2 < m0 → m = 0 ∨ m2 = 0) → m = 0 ∨ m1 = 0 ⊦ m1 +1 = 0, m = 0

Rule argument

indvar: m2

Additional information

Used simplifier rules: nat freely generated by 0, +1;;