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Proof step 44 from proof divi-same (previous step)

m * n2 + n3 = m * n1 ⊦ m * (n1 - n2) = n3, n3 = 0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 45:
m * n2 + n3 = m * n1 ⊦ m * (n1 - n2) = n3, n3 = 0, n2 ≤ n1
Proof step 47:
m * n2 + n3 = m * n1, n1 = n0 + n2, n2 ≤ n1 ⊦ m * n0 = n3, n3 = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n1, n2, n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n1, n2, n