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Proof step 64 from proof add-preserves-reachable-rev (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

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

Rule argument

fma: x0 = []

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ r ∈ H ∧ r ≠ null;%reachnext: ⊦ reachable(r0, H[r0].nxt, H) ↔ r0 ≠ null ∧ r0 ∈ H ∧ H[r0].nxt ∈ H ∧ H[r0].nxt ≠ null;%startnotinH-notreachable: ⊦ ¬ r ∈ H → (reachable(r, r0, H) ↔ false);% ⊦ x0 + [] = x0; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r '.last = r; (s) Used formulas: x0 = []