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Proof step 2 from proof reach-n-split (previous step)

m < n, reachable-n(H, n, r, r0) ⊦ ∃ r1. reachable-n(H, m, r, r1) ∧ reachable-n(H, n - m, r1, r0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
n = n0 + m, m < n, reachable-n(H, n, r, r0), m ≤ n ⊦ ∃ r1. reachable-n(H, m, r, r1) ∧ reachable-n(H, n0, r1, r0)

Rule argument

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

Additional information

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