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Proof step 3 from proof coef-07 (previous step)

m * n + 0 * n ≤ m1 * n + m2 * n ↔ m + 0 ≤ m1 + m2 ∨ n = 0 ⊦ m * n ≤ m1 * n + m2 * n ↔ m ≤ m1 + m2 ∨ n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 0 * n = 0
Proof step 5:
m * n + 0 ≤ m1 * n + m2 * n ↔ m + 0 ≤ m1 + m2 ∨ n = 0 ⊦ m * n ≤ m1 * n + m2 * n ↔ m ≤ m1 + m2 ∨ n = 0

Rule argument

spec: <toplevel> name: zero seq: ⊦ 0 * n = 0 subst: [n] → [n] flags: <all paths>

Additional information

Used terms: n