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Proof step 55 from proof reachable-addnew-rev (previous step)

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

User applied rule exists right

And obtained the following new goals

Proof step 56:
path(ce.nxt ' + x, H[H[r].nxt, ce]), (ce.nxt ' + x).last ∈ H, r ∈ H ⊦ H[r].nxt = ce.nxt, H[r].nxt = null, r = ce.nxt, r = null, r = H[r].nxt, dups(x), reachable(r, (ce.nxt ' + x).last, H), ce.nxt ∈ x, H[r].nxt ∈ x, r ∈ x, H[r].nxt ∈ H, path(ce.nxt ' + x, H) ∧ (ce.nxt ' + x).last = (ce.nxt ' + x).last

Rule argument

pos: right 12 terms: x abort: F discard: T computed: T

Additional information

Used terms: x