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Proof step 15 from proof rem-stays-reachable-aux (previous step)

(r ' + x0).last = H[r].nxt, ce.nxt = H[H[r].nxt].nxt, x0 = r0 + x1, path(r ' + x0, H[r, ce]), H[r].nxt ∈ H[r, ce], r ∈ H, H[r].nxt ∈ H ⊦ H[r].nxt = null, H[r].nxt = ce.nxt, r = null, dups(x0), r ∈ x0, ∃ 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 16:
(ce.nxt ' + 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 ⊦ H[r].nxt = null, H[r].nxt = ce.nxt, r = ce.nxt, r = null, dups(x1), ce.nxt ∈ x1, r ∈ x1, ∃ x. path(H[r].nxt ' + x + H[r].nxt ', H) ∧ ¬ r ∈ x

Rule argument

Additional information

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