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Proof step 3 from proof frommodified (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 4:
reachable(r, r0, H[r, ce]) ⊦ ce.nxt = r, r = null, r = r0, ce.nxt ≠ null ∧ ce.nxt ∈ H ∧ reachable(ce.nxt, r0, H[r, ce])
Proof step 16:
r = r0 ∨ ce.nxt ≠ null ∧ ce.nxt ∈ H ∧ reachable(ce.nxt, r0, H[r, ce]) ⊦ ce.nxt = r, r = null, reachable(r, r0, H[r, ce])

Rule argument

pos: right 2

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