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

x1 ≠ [], x1.last = H[r].nxt, ce.nxt = H[H[r].nxt].nxt, path(ce.nxt ' + x1, H[r, ce]), H[r].nxt ∈ H[r, ce], r ∈ H, H[r].nxt ∈ H ⊦ r = ce.nxt, r = null, H[r].nxt = null, H[r].nxt = ce.nxt, dups(x1), ce.nxt ∈ x1, r ∈ x1, ∃ x. path(H[r].nxt ' + x + H[r].nxt ', H) ∧ ¬ r ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
x1.last = H[r].nxt, ce.nxt = H[x1.last].nxt, path(ce.nxt ' + x1, H[r, ce]), x1.last ∈ H[r, ce], r ∈ H, x1.last ∈ H ⊦ r = ce.nxt, r = null, x1.last = null, x1.last = ce.nxt, x1 = [], dups(x1), ce.nxt ∈ x1, r ∈ x1, ∃ x. path(x1.last ' + x + x1.last ', H) ∧ ¬ r ∈ x

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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