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Proof step 12 from proof rem-reachable (previous step)

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] ⊦ 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]), r ≠ (H[r].nxt ' + x0).last ∧ reachable(H[r1, ce][r].nxt, (H[r].nxt ' + x0).last, H[r1, ce])

User applied rule case distinction

And obtained the following new goals

Proof step 13:
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])

Rule argument

pos: right 6

Additional information

Used simplifier rules: reach-alloc: ⊦ reachable(r, r1, H) → r1 ∈ H;%self-reachable: ⊦ reachable(r, r, H) ↔ ¬ ¬(r ≠ null ∧ r ∈ H);%reachable-notnullinH: ⊦ reachable(r, r1, H) → (¬ r1 ∈ H ↔ false);