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Proof step 22 from proof add-preserves-reachable-rev (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 23:
H[r1].nxt = H[ce.nxt].nxt, reachable(r1, H[r].nxt, H), r1 ∈ H, ce.nxt ∈ H, path(H[r].nxt ' + x, H[r1, ce]), r ∈ H, ∀ H, r1, ce, r. H[r1].nxt = H[ce.nxt].nxt ∧ reachable(r1, H[r].nxt, H) ∧ path(r ' + x, H[r1, ce]) ∧ ce.nxt ∈ H ∧ r1 ∈ H → ce.nxt = null ∨ r1 = null ∨ (ce.nxt ' + x).last = ce.nxt ∨ reachable(r1, ce.nxt, H) ∨ reachable(r1, (r ' + x).last, H) ⊦ x = [], r = null, (H[r].nxt ' + x).last = ce.nxt, r1 = null, ce.nxt = null, r = r1, reachable(r1, (H[r].nxt ' + x).last, H), reachable(r1, ce.nxt, H)

Rule argument

fma: x = []

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null);%app: ⊦ x0 + [] = x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%l: ⊦ r '.last = r; from specification list-last[reflist] Used formulas: x = []