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Proof step 85 from proof rem-stays-reachable-aux (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 86:
ce.nxt = H[H[r0].nxt].nxt, path(H[r0, ce][H[r0].nxt].nxt ' + x + H[r0].nxt ', H[r0, ce]), H[r0].nxt ∈ H[r0, ce], path(r ' + x2 + r0 ', H[r0, ce]), r0 ∈ H, H[r0].nxt ∈ H, path(r ' + x2 + r0 ', H) ⊦ r0 = H[r0, ce][H[r0].nxt].nxt, r = r0, H[r0].nxt = null, H[r0].nxt = ce.nxt, r0 = null, path(r ' + x2 + r0 ' + (H[r0, ce][H[r0].nxt].nxt ' + x) + H[r0].nxt ', H[r0, ce]), dups(x2), r0 ∈ x2, r ∈ x2, r0 ∈ x, 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);%At-other: ⊦ r ≠ r0 → H[r0, ce][r] = H[r]; from specification store[linheap]%At-same: ⊦ H[r, ce][r] = ce; from specification store[linheap]%insin: ⊦ r ∈ H[r, ce]; from specification store[linheap]%in-06: ⊦ ¬ r ∈ r0 ' + x0 ↔ r ≠ r0 ∧ ¬ r ∈ x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]