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Proof step 83 from proof rem-stays-reachable-aux (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 84:
ce.nxt = H[H[r0].nxt].nxt, H[r0, ce][H[r0].nxt].nxt = H[r0].nxt, path(r ' + x2 + r0 ', H[r0, ce]), path(r ' + x2 + r0 ', H), H[r0].nxt ∈ H, r0 ∈ H, H[r0].nxt ∈ H[r0, ce] ⊦ H[r0].nxt = ce.nxt, H[r0].nxt = null, r = r0, dups(x2), path(r ' + x2 + r0 ' + H[r0].nxt ', H[r0, ce]), r0 ∈ x2, r ∈ x2

Rule argument

Additional information

Used simplifier rules: path-two: ⊦ path(r ' + r0 ', H) ↔ r ∈ H ∧ r0 ∈ H ∧ r ≠ null ∧ r0 ≠ null ∧ H[r].nxt = r0;% ⊦ H[r, ce][r] = ce; (s)% ⊦ r ∈ H[r, ce]; (s)% ⊦ ¬ r ∈ []; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ [] + x0 = x0; (s)