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Proof step 61 from proof add-preserves-reachable-rev (previous step)

H[r1].nxt = H[ce.nxt].nxt, reachable(r, r1, H), reachable(H[r].nxt, ce.nxt, H), (H[r].nxt ' + x0).last ∈ H[r1, ce], r1 ∈ H, path(H[r].nxt ' + x0, H[r1, ce]), r ∈ H, ce.nxt ∈ H ⊦ r = null, (H[r].nxt ' + x0).last = ce.nxt, ce.nxt = null, r = r1, 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 62:
H[r1].nxt = H[ce.nxt].nxt, reachable(r, r1, H), reachable(H[r].nxt, ce.nxt, H), (H[r].nxt ' + x0).last ∈ H[r1, ce], r1 ∈ H, path(H[r].nxt ' + x0, H[r1, ce]), r ∈ H, ce.nxt ∈ H ⊦ x0 = [], r = null, (H[r].nxt ' + x0).last = ce.nxt, ce.nxt = null, r = r1, reachable(r, (H[r].nxt ' + x0).last, H), reachable(r, ce.nxt, 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);%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: x0 = []