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Proof step 12 from proof mod-nle (previous step)

n < n0, m0 < m, m * n0 + n2 ≤ m0 * n + n1, n1 < n0, n1 < n, n2 < n0, n1 + 1 < n0 ⊦ n = 0, n0 = 0, m = 0, n = n0

User applied rule insert lemma

And obtained the following new goals

Proof step 13:
⊦ n2 < n ∧ m1 < m ∧ n1 < n → m1 * n + n1 < m * n + n2
Proof step 14:
n2 < n0 ∧ m0 < m ∧ n1 < n0 → m0 * n0 + n1 < m * n0 + n2, n < n0, m0 < m, m * n0 + n2 ≤ m0 * n + n1, n1 < n0, n1 < n, n2 < n0, n1 + 1 < n0 ⊦ n = 0, n0 = 0, m = 0, n = n0

Rule argument

spec: nat-mult inst: 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] flags: current, []

Additional information

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