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Proof step 1 from proof coef-21 (conclusion)

⊦ m * n < m1 * n + n ↔ m < m1 + 1 ∧ n ≠ 0

User applied rule apply lemma

And obtained the following new goals

Proof step 2:
⊦ m * n < m1 * n + m2 * n ↔ m < m1 + m2 ∧ n ≠ 0
Proof step 3:
m * n < m1 * n + 1 * n ↔ m < m1 + 1 ∧ n ≠ 0 ⊦ m * n < m1 * n + n ↔ m < m1 + 1 ∧ n ≠ 0

Rule argument

spec: <toplevel> name: coef-08 seq: ⊦ m * n < m1 * n + m2 * n ↔ m < m1 + m2 ∧ n ≠ 0 subst: [m, n, m1, m2] → [m, n, m1, 1]

Additional information

Used terms: m, n, m1, 1