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Proof step 86 from proof rem-stays-reachable-aux (previous step)

ce.nxt = H[H[r0].nxt].nxt, x1 = r1 + x, 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 87:
ce.nxt = H[H[r0].nxt].nxt, path(H[r0, ce][H[r0].nxt].nxt ' + x + H[r0].nxt ', H[r0, ce]), path(r ' + x2 + r0 ', H), path(r ' + x2 + r0 ', H[r0, ce]), H[r0].nxt ∈ H[r0, ce], r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = null, H[r0].nxt = ce.nxt, r = r0, r0 = H[r0, ce][H[r0].nxt].nxt, r0 = null, dups(x2), path(r ' + x2 + r0 ' + (H[r0, ce][H[r0].nxt].nxt ' + x) + H[r0].nxt ', H[r0, ce]), r0 ∈ x, r ∈ x2, r0 ∈ x2, path(ce.nxt ' + x + H[r0].nxt ', H[r0, ce]) ∧ ce.nxt = H[r0, ce][H[r0].nxt].nxt

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);%path-last-not-null: ⊦ ¬ path(r ' + x + null ', H);% ⊦ r ≠ r0 → H[r0, ce][r] = H[r]; (s)% ⊦ H[r, ce][r] = ce; (s)% ⊦ r ∈ H[r, ce]; (s)% ⊦ r ∈ r0 ' + x0 ↔ ¬(r ≠ r0 ∧ ¬ r ∈ x0); (ss)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r + x0 = r ' + x0; (s)