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Proof step 2 from proof mod-nls (previous step)

n1 < n0, n1 < n, n2 < n0, n ≤ n0, m0 < m, m * n0 + n2 < m0 * n + n1 ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ m0 < m ∧ n ≤ n0 ∧ n2 < n0 ∧ n1 < n → ¬ m * n0 + n2 ≤ m0 * n + n1
Proof step 4:
m0 < m ∧ n ≤ n0 ∧ n2 < n0 ∧ n1 < n → ¬ m * n0 + n2 ≤ m0 * n + n1, n1 < n0, n1 < n, n2 < n0, n ≤ n0, m0 < m, m * n0 + n2 < m0 * n + n1 ⊦

Rule argument

spec: nat-mult inst: name: mod-nle seq: ⊦ m0 < m ∧ n ≤ n0 ∧ n2 < n0 ∧ n1 < n → ¬ m * n0 + n2 ≤ m0 * n + n1 subst: [m0, m, n, n0, n2, n1] → [m0, m, n, n0, n2, n1] flags: current, []

Additional information

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