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Proof step 7 from proof mod-nle (previous step)

m * n0 + n2 < m0 * n0 + n1, n1 < n0, n2 < n0, m0 < m ⊦ m * n0 + n2 = m0 * n0 + n1

User applied rule apply lemma

And obtained the following new goals

Proof step 8:
⊦ n2 < n ∧ m1 < m ∧ n1 < n → m1 * n + n1 < m * n + n2
Proof step 9:
m0 < m, n2 < n0, n1 < n0, m * n0 + n2 < m0 * n0 + n1, n2 < n0 ∧ m0 < m ∧ n1 < n0 → m0 * n0 + n1 < m * n0 + n2 ⊦ m * n0 + n2 = m0 * n0 + n1

Rule argument

spec: <toplevel> name: modls-03 seq: ⊦ n2 < n ∧ m1 < m ∧ n1 < n → m1 * n + n1 < m * n + n2 subst: [n2, n, m1, m, n1] → [n2, n0, m0, m, n1]

Additional information

Used terms: n2, n0, m0, m, n1