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Proof step 6 from proof path-last (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 7:
path(H[r].nxt ' + x0, H), r ∈ H, ∀ r, H. path(r ' + x0, H) → x0 = [] ∨ x0.last ∈ H ⊦ x0 = [], r = null, (H[r].nxt ' + x0).last ∈ H

Rule argument

fma: x0 = []

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: x0 = []