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Proof step 36 from proof rem-stays-reachable-aux1 (previous step)

path(H[H[r0].nxt].nxt ' + x0 + H[r0].nxt ', H), r0 ∈ H, H[r0].nxt ∈ H, ∃ x. path(H[H[r0].nxt].nxt ' + x, H) ∧ (H[H[r0].nxt].nxt ' + x).last = r0 ∧ ¬ dups(H[H[r0].nxt].nxt ' + x) ⊦ H[r0].nxt = H[H[r0].nxt].nxt, H[r0].nxt = null, r0 = H[H[r0].nxt].nxt, r0 ∈ x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
(H[H[r0].nxt].nxt ' + x).last = r0, path(H[H[r0].nxt].nxt ' + x, H), path(H[H[r0].nxt].nxt ' + x0 + H[r0].nxt ', H), H[r0].nxt ∈ H, r0 ∈ H ⊦ H[r0].nxt = null, H[r0].nxt = H[H[r0].nxt].nxt, r0 = H[H[r0].nxt].nxt, dups(x), r0 ∈ x0, H[H[r0].nxt].nxt ∈ x

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ dups(r ' + x0) ↔ dups(x0) ∨ r ∈ x0; (ws)