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Proof step 34 from proof reachable-addnew-rev (previous step)

path(r ' + x1 + r2 ' + x0, H[r2, ce]), r ∈ H, (r2 ' + x0).last ∈ H ⊦ r2 ∈ H, r ∈ x1, r ∈ x0, r2 ∈ x1, r2 ∈ x0, dups(x1 + x0), reachable(r, (r2 ' + x0).last, H), dups(x1), dups(x0), ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ H[r0].nxt ≠ null ∧ reachable(ce.nxt, (H[r0].nxt ' + x0).last, H)

User applied rule exists right

And obtained the following new goals

Proof step 35:
path(r ' + x1 + r2 ' + x0, H[r2, ce]), r ∈ H, (r2 ' + x0).last ∈ H ⊦ r2 ∈ H, r ∈ x1, r ∈ x0, r2 ∈ x1, r2 ∈ x0, dups(x1 + x0), reachable(r, (r2 ' + x0).last, H), dups(x1), dups(x0), reachable(r, (r + x1).last, H) ∧ H[(r + x1).last].nxt = r2 ∧ H[(r + x1).last].nxt ≠ null ∧ reachable(ce.nxt, (H[(r + x1).last].nxt ' + x0).last, H)

Rule argument

pos: right 10 terms: (r + x1).last abort: F discard: T computed: F

Additional information

Used terms: (r + x1).last