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Proof step 55 from proof divi-same (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 56:
m * n2 = m * n1 + n3 ⊦ m * (n2 - n1) = n3, n1 ≤ n2
Proof step 58:
m * n2 = m * n1 + n3, n2 = n0 + n1, n1 ≤ n2 ⊦ m * n0 = n3

Rule argument

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

Additional information

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