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Proof step 14 from proof acyclic-rem-not-reachable (previous step)

ce.nxt = H[H[r0].nxt].nxt, path(r ' + x1 + H[r0].nxt ', H[r0, ce]), reachable(r, r0, H), H[r0].nxt ∈ H[r0, ce], r0 ∈ H, H[r0].nxt ∈ H, r0 ∈ x1, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r0].nxt = null, r = H[r0].nxt, dups(x1), H[r0].nxt ∈ x1, r ∈ x1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ r ∈ x0 ↔ (∃ x1, x2. x0 = x1 + r ' + x2 ∧ ¬ r ∈ x2)
Proof step 16:
ce.nxt = H[H[r0].nxt].nxt, path(r ' + x1 + H[r0].nxt ', H[r0, ce]), reachable(r, r0, H), H[r0].nxt ∈ H, r0 ∈ H, H[r0].nxt ∈ H[r0, ce], ∀ r1. ¬ reachable(H[r1].nxt, r1, H), ∃ x, x2. x1 = x + r0 ' + x2 ∧ ¬ r0 ∈ x2 ⊦ H[r0].nxt = null, r = H[r0].nxt, dups(x1), r ∈ x1, H[r0].nxt ∈ x1

Rule argument

spec: list, inst: reflist name: lastoc-rew seq: ⊦ r ∈ x0 ↔ (∃ x1, x2. x0 = x1 + r ' + x2 ∧ ¬ r ∈ x2) subst: [x0, r] → [x1, r0] flags: <all paths>

Additional information

Used terms: x1, r0