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Proof step 13 from proof acyclic-rem-not-reachable (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ r ∈ x0 ↔ (∃ x1, x2. x0 = x1 + r ' + x2 ∧ ¬ r ∈ x2)
Proof step 15:
∃ x, x2. x1 = x + r0 ' + x2 ∧ ¬ r0 ∈ x2, ce.nxt = H[H[r0].nxt].nxt, path(r ' + x1 + H[r0].nxt ', H[r0, ce]), reachable(r, r0, H), H[r0].nxt ∈ H, H[r0].nxt ∈ H[r0, ce], r0 ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r0].nxt = null, r = H[r0].nxt, r ∈ x1, H[r0].nxt ∈ x1, dups(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: rewrite

Additional information

Used terms: x1, r0