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Proof step 8 from proof mod-eq-01 (previous step)

m0 < n, n0 < n ⊦ (m0 + n0) % n = m0 ↔ n0 = 0, n = 0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n
Proof step 10:
m0 + n0 = m1 * n + n1, n0 < n, m0 < n, n1 < n ⊦ n1 = m0 ↔ n0 = 0, n = 0

Rule argument

spec: <toplevel> name: div-elim seq: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n subst: [m, n, m0, n0] → [m0 + n0, n, m, n1] flags: <rotated> <all paths>

Additional information

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