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Proof step 17 from proof rem-stays-reachable-aux1 (previous step)

path(H[H[r0].nxt].nxt ' + x1 + H[r0].nxt ', H), r0 ∈ H, H[r0].nxt ∈ H, r0 ∈ x1 ⊦ H[r0].nxt = H[H[r0].nxt].nxt, H[r0].nxt = null, dups(x1), reachable(H[H[r0].nxt].nxt, r0, H), H[H[r0].nxt].nxt ∈ x1, H[r0].nxt ∈ x1, ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ r ∈ x0 ↔ (∃ x1, x2. x0 = x1 + (r + x2))
Proof step 19:
path(H[H[r0].nxt].nxt ' + x1 + H[r0].nxt ', H), H[r0].nxt ∈ H, r0 ∈ H, ∃ x, x2. x1 = x + (r0 + x2) ⊦ H[r0].nxt = null, H[r0].nxt = H[H[r0].nxt].nxt, dups(x1), reachable(H[H[r0].nxt].nxt, r0, H), H[r0].nxt ∈ x1, H[H[r0].nxt].nxt ∈ x1, ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

Rule argument

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

Additional information

Used terms: x1, r0