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Proof step 24 from proof add-preserves-reachable-rev (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
H[r1].nxt = H[ce.nxt].nxt, path(H[r].nxt ' + x, H[r1, ce]), reachable(r1, H[r].nxt, H), r1 ∈ H, ce.nxt ∈ H, r ∈ H, ∀ H0, r0, ce0, r2. H0[r0].nxt = H0[ce0.nxt].nxt ∧ path(r2 ' + x, H0[r0, ce0]) ∧ reachable(r0, H0[r2].nxt, H0) ∧ ce0.nxt ∈ H0 ∧ r0 ∈ H0 → x.last = ce0.nxt ∨ ce0.nxt = null ∨ r0 = null ∨ reachable(r0, x.last, H0) ∨ reachable(r0, ce0.nxt, H0) ⊦ x.last = ce.nxt, ce.nxt = null, r = r1, r = null, r1 = null, x = [], reachable(r1, ce.nxt, H), reachable(r1, x.last, H)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ x0 ≠ [] → (r ' + x0).last = x0.last; (s)