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Proof step 8 from proof add-preserves-reachable (previous step)

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

User applied rule all left

And obtained the following new goals

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

Rule argument

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

Additional information

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