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Proof step 171 from proof rem-stays-reachable-aux2 (previous step)

(r1 ' + x0).last = (r ' + x).last, H[(r ' + x).last].nxt = H[r1].nxt, path(r1 ' + x0, H), path(r ' + x + H[r1].nxt ' + (r0 ' + x3) + r1 ', H), path(r ' + x, H), path(H[r1].nxt ' + (r0 ' + x3) + r1 ', H), r1 ∈ H, (r ' + x).last ∈ H, H[r1].nxt ∈ H ⊦ H[r1].nxt = r1, H[r1].nxt = r0, H[r1].nxt = null, r = H[r1].nxt, r = r0, r1 = r, r1 = r0, dups(x0), dups(x + x3), dups(x), dups(x3), r1 ∈ x3, H[r1].nxt ∈ x3, H[r1].nxt ∈ x, r1 ∈ x, r1 ∈ x0, r ∈ x, r ∈ x3, r0 ∈ x3, r0 ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 172:
(r1 ' + x0).last = (r ' + x).last, H[(r ' + x).last].nxt = H[r1].nxt, path(H[H[r1].nxt].nxt ' + x3 + r1 ', H), path(r1 ' + x0, H), path(r ' + x + H[r1].nxt ' + (H[H[r1].nxt].nxt ' + x3) + r1 ', H), path(r ' + x, H), r1 ∈ H, (r ' + x).last ∈ H, H[r1].nxt ∈ H ⊦ H[r1].nxt = r1, H[r1].nxt = H[H[r1].nxt].nxt, H[r1].nxt = null, r = H[r1].nxt, r = H[H[r1].nxt].nxt, r1 = r, r1 = H[H[r1].nxt].nxt, dups(x0), dups(x + x3), dups(x), dups(x3), r1 ∈ x3, H[r1].nxt ∈ x3, H[r1].nxt ∈ x, r1 ∈ x, r1 ∈ x0, r ∈ x, r ∈ x3, H[H[r1].nxt].nxt ∈ x3, H[H[r1].nxt].nxt ∈ x

Rule argument

Additional information

Used simplifier rules: path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H);%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]