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Proof step 14 from proof rem-stays-reachable-aux (previous step)

x0 = r0 + x1, ce.nxt = H[H[r].nxt].nxt, (r ' + x0).last = H[r].nxt, path(r ' + x0, H[r, ce]), H[r].nxt ∈ H, r ∈ H, H[r].nxt ∈ H[r, ce] ⊦ H[r].nxt = ce.nxt, H[r].nxt = null, r = null, r ∈ x0, dups(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 15:
(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 ⊦ 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

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));%rec: ⊦ dups(r ' + x0) ↔ ¬ ¬(r ∈ x0 ∨ dups(x0)); from specification list-dup[reflist]%in-06: ⊦ ¬ r ∈ r0 ' + x0 ↔ r ≠ r0 ∧ ¬ r ∈ x0; from specification list[reflist]%At-same: ⊦ H[r, ce][r] = ce; from specification store[linheap]%insin: ⊦ r ∈ H[r, ce]; from specification store[linheap]%l-05: ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; from specification list-last[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]