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

¬ r ≠ r1, ce.nxt = H[H[r1].nxt].nxt, (H[r].nxt ' + x0).last ∈ H[r1, ce], reachable(H[r].nxt, (H[r].nxt ' + x0).last, H[r1, ce]), r ∈ H, path(H[r].nxt ' + x0, H), H[r1].nxt ∈ H, r1 ∈ H, (H[r].nxt ' + x0).last ∈ H, r ∈ H[r1, ce] ⊦ reachable(H[r1, ce][r].nxt, (H[r].nxt ' + x0).last, H[r1, ce]), r1 = null, H[r1].nxt = null, (H[r].nxt ' + x0).last = H[r1].nxt, r = null, reachable(r, (H[r].nxt ' + x0).last, H[r1, ce])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
ce.nxt = H[H[r1].nxt].nxt, reachable(H[r1].nxt, (H[r1].nxt ' + x0).last, H[r1, ce]), path(H[r1].nxt ' + x0, H), H[r1].nxt ∈ H, r1 ∈ H, (H[r1].nxt ' + x0).last ∈ H, (H[r1].nxt ' + x0).last ∈ H[r1, ce] ⊦ H[r1].nxt = null, (H[r1].nxt ' + x0).last = H[r1].nxt, r1 = null, reachable(r1, (H[r1].nxt ' + x0).last, H[r1, ce]), reachable(ce.nxt, (H[r1].nxt ' + x0).last, H[r1, ce])

Rule argument

Additional information

Used simplifier rules: reach-alloc: ⊦ reachable(r, r1, H) → r1 ∈ H;%At-same: ⊦ H[r, ce][r] = ce; from specification store[linheap]%insin: ⊦ r ∈ H[r, ce]; from specification store[linheap]