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Proof step 2 from proof rem-reachable-rev (previous step)

ce.nxt = H[H[r1].nxt].nxt, H[r1].nxt ∈ H, r1 ∈ H ⊦ H[r1].nxt = null, reachable(r, r0, H[r1, ce]) ↔ reachable(r, r0, H), r0 = H[r1].nxt, r1 = null

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: rem-reachable-rev-weak: ⊦ reachable(r, r0, H[r1, ce]) ∧ ce.nxt = H[H[r1].nxt].nxt ∧ r0 ≠ H[r1].nxt ∧ H[r1].nxt ∈ H ∧ H[r1].nxt ≠ null ∧ r1 ≠ null ∧ r1 ∈ H → (reachable(r, r0, H) ↔ true);%rem-reachable: ⊦ reachable(r, r0, H) ∧ ce.nxt = H[H[r1].nxt].nxt ∧ r0 ≠ H[r1].nxt ∧ H[r1].nxt ∈ H ∧ H[r1].nxt ≠ null ∧ r1 ≠ null ∧ r1 ∈ H → (reachable(r, r0, H[r1, ce]) ↔ true);