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Proof step 25 from proof rem-stays-reachable-aux (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
(r ' + x0).last = H[x.last].nxt, ce.nxt = H[H[x.last].nxt].nxt, path(r ' + x0, H[x.last, ce]), path(r ' + x, H), H[x.last].nxt ∈ H, x.last ∈ H, H[x.last].nxt ∈ H[x.last, ce] ⊦ H[x.last].nxt = ce.nxt, H[x.last].nxt = null, x = [], dups(x), dups(x0), r ∈ x, r ∈ x0, ∃ x0. path(H[x.last].nxt ' + x0 + H[x.last].nxt ', H) ∧ ¬ x.last ∈ x0, ∃ x0. path(r ' + x0 + H[x.last].nxt ', H) ∧ x.last ≠ r ∧ ¬ x.last ∈ x0, H[x.last].nxt ≠ x.last ∧ r = H[x.last].nxt

Proof step 25 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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