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Proof step 6 from proof modnotreachable-reachable-rev-weak (previous step)

∀ r0, H, r, ce. r0 ∈ H ∧ path(r ' + x0, H[r0, ce]) → r0 = null ∨ reachable(r, (r ' + x0).last, H) ∨ reachable(r, r0, H), r0 ∈ H, path(r ' + (r1 + x0), H[r0, ce]) ⊦ r0 = null, reachable(r, (r ' + (r1 + x0)).last, H), reachable(r, r0, H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
path(H[r0, ce][r].nxt ' + x0, H[r0, ce]), r ∈ H[r0, ce], r0 ∈ H, ∀ r0, H, r, ce. r0 ∈ H ∧ path(r ' + x0, H[r0, ce]) → r0 = null ∨ reachable(r, (r ' + x0).last, H) ∨ reachable(r, r0, H) ⊦ r = null, r0 = null, reachable(r, (H[r0, ce][r].nxt ' + x0).last, H), reachable(r, r0, 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));%l-05: ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; from specification list-last[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]