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

path(H[r].nxt ' + x0, H[r0, ce]), r ∈ H, r0 ∈ H, (H[r].nxt ' + x0).last ∈ H[r0, ce], path(H[r].nxt ' + x0, H[r0, ce]) ∧ r0 ∈ H → reachable(H[r].nxt, r0, H) ∨ reachable(H[r].nxt, (H[r].nxt ' + x0).last, H) ⊦ r = null, r = r0, 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, (H[r].nxt ' + x0).last ∈ H[r0, ce], (H[r].nxt ' + x0).last ∈ H ⊦ r = null, r = r0, 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);%reach-alloc: ⊦ reachable(r, r1, H) → r1 ∈ H;