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Proof step 8 from proof reachable-addnew-rev (previous step)

r1 = r2, reachable(r, r1, H[r2, ce]), r ∈ H, r1 = r2 ∨ r1 ∈ H ⊦ reachable(r, r1, H), r2 ∈ H, ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ H[r0].nxt ≠ null ∧ (r1 = H[r0].nxt ∨ reachable(ce.nxt, r1, H))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
reachable(r, r2, H[r2, ce]), r ∈ H ⊦ r2 ∈ H, ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ H[r0].nxt ≠ null

Rule argument

Additional information

Used simplifier rules: endnotinH-notreachable: ⊦ ¬ r0 ∈ H → (reachable(r, r0, H) ↔ false);%reach-alloc: ⊦ reachable(r, r1, H) → r1 ∈ H;% ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; (ws)