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Proof step 6 from proof cyclic-all-cyclic (previous step)

reachable-n(H, m0, H[r] .nxt, r0), r ∈ H, H[r] .nxt ∈ H, reachable-n(H, m, H[r] .nxt, r) ⊦ H[r] .nxt = null, r = null, reachable-n(H, m + 1, r0, r0), ∃ r1. reachable-n(H, m, H[r] .nxt, r1) ∧ reachable-1(H, r1, H[r] .nxt)

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

[EXRARG : pos: right 4, [QUANTTERMLIST : (r)]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ reachable-1(H, r, r0) ↔ r ≠ null ∧ r0 ≠ null ∧ r ∈ H ∧ r0 ∈ H ∧ H[r] .nxt = r0])], [EXTRATERMS : (r)]]