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Proof step 43 from proof rem-stays-reachable-aux (previous step)

¬ r0 ∈ ce.nxt ' + x2 ∧ r0 ∈ H, ce.nxt = H[H[r0].nxt].nxt, path(r ' + x0 + r0 ' + (ce.nxt ' + x2) + H[r0].nxt ', H[r0, ce]), path((ce.nxt ' + x2) + H[r0].nxt ', H), path(r ' + x0 + r0 ', H[r0, ce]), H[r0].nxt ∈ H, r0 ∈ H, path(r ' + x1 + r0 ', H) ⊦ r0 = ce.nxt, r = ce.nxt, r0 = null, H[r0].nxt = r0, r = r0, r = H[r0].nxt, H[r0].nxt = null, H[r0].nxt = ce.nxt, dups(x2), dups(x0), dups(x0 + x2), ce.nxt ∈ x2, ce.nxt ∈ x0, r0 ∈ x2, H[r0].nxt ∈ x2, H[r0].nxt ∈ x0, r ∈ x2, r ∈ x0, dups(x1), r0 ∈ x1, r ∈ x1, r0 ∈ x0, ∃ x. path(r ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x, ∃ x0. path(H[r0].nxt ' + x0 + H[r0].nxt ', H) ∧ ¬ r0 ∈ x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
ce.nxt = H[H[r0].nxt].nxt, path(r ' + x0 + r0 ' + (ce.nxt ' + x2) + H[r0].nxt ', H[r0, ce]), path((ce.nxt ' + x2) + H[r0].nxt ', H), path(r ' + x0 + r0 ', H[r0, ce]), H[r0].nxt ∈ H, r0 ∈ H, path(r ' + x1 + r0 ', H) ⊦ r0 = ce.nxt, r = ce.nxt, r0 = null, H[r0].nxt = r0, r = r0, r = H[r0].nxt, H[r0].nxt = null, H[r0].nxt = ce.nxt, dups(x2), dups(x0), dups(x0 + x2), ce.nxt ∈ x2, ce.nxt ∈ x0, H[r0].nxt ∈ x2, H[r0].nxt ∈ x0, r ∈ x2, r ∈ x0, dups(x1), r0 ∈ x1, r ∈ x1, r0 ∈ x0, r0 ∈ x2, ∃ x. path(r ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x, ∃ x0. path(H[r0].nxt ' + x0 + H[r0].nxt ', H) ∧ ¬ r0 ∈ x0

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%in-01: ⊦ r ≠ r0 → (r ∈ r0 ' + x0 ↔ r ∈ x0); from specification list[reflist]