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Proof step 59 from proof add-preserves-reachable-rev (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 60:
reachable(H[r].nxt, ce.nxt, H), r ≠ r1, H[r1].nxt = H[ce.nxt].nxt, (H[r].nxt ' + x0).last ∈ H[r1, ce], r1 ∈ H, path(H[r].nxt ' + x0, H[r1, ce]), r ∈ H[r1, ce], reachable(r, r1, H), ce.nxt ∈ H ⊦ r = null, (H[r].nxt ' + x0).last = ce.nxt, ce.nxt = null, reachable(r, (H[r].nxt ' + x0).last, H), reachable(r, ce.nxt, H)
Proof step 65:
reachable(H[r].nxt, (H[r].nxt ' + x0).last, H), r ≠ r1, H[r1].nxt = H[ce.nxt].nxt, (H[r].nxt ' + x0).last ∈ H[r1, ce], r1 ∈ H, path(H[r].nxt ' + x0, H[r1, ce]), r ∈ H[r1, ce], reachable(r, r1, H), ce.nxt ∈ H ⊦ r = null, (H[r].nxt ' + x0).last = ce.nxt, ce.nxt = null, reachable(r, (H[r].nxt ' + x0).last, H), reachable(r, ce.nxt, H)

Rule argument

pos: left 1

Proof step 59 from proof add-preserves-reachable-rev (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information