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Proof step 8 from proof null-not-reachable (previous step)

∀ r, H. x0.last = null ∧ path(r ' + x0, H) ∧ null ∈ H → x0 = [], (r0 + x0).last = null, path(r ' + (r0 + x0), H), null ∈ H ⊦ r0 + x0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
x0.last = null, path(H[r].nxt ' + x0, H), r ∈ H, null ∈ H ⊦ r = null, x0 = [], ∃ r, H. path(r ' + x0, H) ∧ null ∈ H

Rule argument

Additional information

Used simplifier rules: path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H));%path-one: ⊦ path(r ', H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null);%l-02: ⊦ x0 ≠ [] → (r ' + x0).last = x0.last; from specification list-last[reflist]%l: ⊦ r '.last = r; from specification list-last[reflist]%app: ⊦ x0 + [] = x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%e-01: ⊦ r ' + x0 ≠ []; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]