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Proof step 35 from proof rem-stays-reachable-aux1 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
(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 ⊦ r0 = H[H[r0].nxt].nxt, H[r0].nxt = null, H[r0].nxt = H[H[r0].nxt].nxt, r0 ∈ x0, H[H[r0].nxt].nxt ∈ x, dups(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]