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Proof step 56 from proof rem-stays-reachable-aux (previous step)

ce.nxt = H[H[(r ' + x).last].nxt].nxt, path(r ' + x0 + H[(r ' + x).last].nxt ', H), path(r ' + x, H), H[(r ' + x).last].nxt ∈ H, (r ' + x).last ∈ H ⊦ H[(r ' + x).last].nxt = ce.nxt, H[(r ' + x).last].nxt = null, (r ' + x).last = r, r ∈ x, dups(x), (r ' + x).last ∈ x0, ∃ x0. path(r ' + x0, H[(r ' + x).last, ce]) ∧ (r ' + x0).last = H[(r ' + x).last].nxt

User applied rule exists right

And obtained the following new goals

Proof step 57:
ce.nxt = H[H[(r ' + x).last].nxt].nxt, path(r ' + x0 + H[(r ' + x).last].nxt ', H), path(r ' + x, H), H[(r ' + x).last].nxt ∈ H, (r ' + x).last ∈ H ⊦ H[(r ' + x).last].nxt = ce.nxt, H[(r ' + x).last].nxt = null, (r ' + x).last = r, r ∈ x, dups(x), (r ' + x).last ∈ x0, path(r ' + x0 + H[(r ' + x).last].nxt ', H[(r ' + x).last, ce]) ∧ (r ' + x0 + H[(r ' + x).last].nxt ').last = H[(r ' + x).last].nxt

Rule argument

pos: right 7 terms: x0 + H[(r ' + x).last].nxt ' abort: F discard: T computed: F

Additional information

Used terms: x0 + H[(r ' + x).last].nxt '