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Proof step 8 from proof rem-reachable (previous step)

ce.nxt = H[H[r1].nxt].nxt, path(H[r].nxt ' + x0, H), r ∈ H, H[r1].nxt ∈ H, r1 ∈ H, ∀ ce, H, r1, r. ce.nxt = H[H[r1].nxt].nxt ∧ path(r ' + x0, H) ∧ r1 ∈ H ∧ H[r1].nxt ∈ H → (r ' + x0).last = H[r1].nxt ∨ H[r1].nxt = null ∨ r1 = null ∨ reachable(r, (r ' + x0).last, H[r1, ce]) ⊦ (H[r].nxt ' + x0).last = H[r1].nxt, H[r1].nxt = null, r = null, r1 = null, reachable(r, (H[r].nxt ' + x0).last, H[r1, ce])

User applied rule all left

And obtained the following new goals

Proof step 9:
ce.nxt = H[H[r1].nxt].nxt, path(H[r].nxt ' + x0, H), r1 ∈ H, H[r1].nxt ∈ H, r ∈ H, ce.nxt = H[H[r1].nxt].nxt ∧ path(H[r].nxt ' + x0, H) ∧ r1 ∈ H ∧ H[r1].nxt ∈ H → (H[r].nxt ' + x0).last = H[r1].nxt ∨ H[r1].nxt = null ∨ r1 = null ∨ reachable(H[r].nxt, (H[r].nxt ' + x0).last, H[r1, ce]) ⊦ (H[r].nxt ' + x0).last = H[r1].nxt, H[r1].nxt = null, r = null, r1 = null, reachable(r, (H[r].nxt ' + x0).last, H[r1, ce])

Rule argument

pos: left 6 terms: ce, H, r1, H[r].nxt abort: F discard: T computed: T

Additional information

Used terms: ce, H, r1, H[r].nxt