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Proof step 5 from proof removed-stays-reachable (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 6:
reachable(r, r0, H[r0, ce]), ce.nxt = H[ce.nxt].nxt, ce.nxt = H[r0].nxt, r0 ∈ H, ce.nxt ∈ H, reachable(r, r0, H) ⊦ ce.nxt = null, reachable(r, ce.nxt, H[r0, ce])

Rule argument

fma: reachable(r, r0, H[r0, ce])

Additional information

Used simplifier rules: changenonnxt-reachable: ⊦ reachable(r, r0, H) ∧ ce.nxt = H[r1].nxt → (¬ reachable(r, r0, H[r1, ce]) ↔ false); Used formulas: reachable(r, r0, H[r0, ce])