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Proof step 4 from proof square-two (previous step)

n * n + n ≤ n * 2, n * n + n = m * 2, m ≤ n ⊦ n = m ∧ m < 2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ m * n + n ≤ m1 * n ↔ ¬ ¬(m + 1 ≤ m1 ∨ n = 0)
Proof step 6:
n + 1 ≤ 2 ∨ n = 0, n * n + n = m * 2, m ≤ n ⊦ n = m ∧ m < 2

Rule argument

spec: nat-mult inst: name: coef-18 seq: ⊦ m * n + n ≤ m1 * n ↔ ¬ ¬(m + 1 ≤ m1 ∨ n = 0) subst: [m1, n, m] → [2, n, n] flags: rewrite, current

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; Used terms: 2, n, n