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Proof step 12 from proof modnotreachable-reachable-rev-weak (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
path(H[r].nxt ' + x0, H[r0, ce]), reachable(H[r].nxt, (H[r].nxt ' + x0).last, H), r ∈ H, r0 ∈ H ⊦ r = null, r = r0, r0 = null, reachable(r, r0, H), reachable(r, (H[r].nxt ' + x0).last, H), reachable(H[r].nxt, r0, H)

Rule argument

Additional information

Used simplifier rules: fromnext-reachable-rev: ⊦ reachable(H[r].nxt, r0, H) ∧ r ≠ r0 ∧ r ≠ null ∧ r ∈ H → (reachable(r, r0, H) ↔ true);