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

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

User applied rule case distinction

And obtained the following new goals

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

Rule argument

pos: left 8

Additional information

Used simplifier rules: fromnext-reachable: ⊦ reachable(r, r0, H) ∧ r ≠ r0 → (reachable(H[r].nxt, r0, H) ↔ true);% ⊦ r ≠ r0 → (r ∈ H[r0, ce] ↔ r ∈ H); (s)