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Proof step 6 from proof rem-stays-reachable-aux1 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
(H[H[r0].nxt].nxt ' + x).last = H[r0].nxt, path(H[H[r0].nxt].nxt ' + x, H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = H[H[r0].nxt].nxt, H[r0].nxt = null, reachable(H[H[r0].nxt].nxt, r0, H), H[H[r0].nxt].nxt ∈ x, dups(x), ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

Rule argument

Additional information

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