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Proof step 14 from proof divi-same (previous step)

m * n2 = n - m0, m * n1 = dist(n0, m0), m0 < n ⊦ m | dist(n, n0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 15:
m * n1 = dist(n0, m0), m * n2 = n3, n = n3 + m0, m0 < n, m0 ≤ n ⊦ m | dist(n, n0)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n, m0, n3]

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < n → ¬ n < m; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, m0, n3