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Proof step 9 from proof legal-noncylic-equiv-reaches-null (previous step)

H[r0] .nxt = null, legal(H), r ∈ H, reachable-n(H, n0, r, r0) ⊦ r = null, r ≠ null ∧ r ∈ H ∧ (∃ n. reachable-n(H, n, r, r0)), ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null

User applied rule constructor cut

And obtained the following new goals

Proof step 8:
n0 = m +1, H[r0] .nxt = null, legal(H), r ∈ H, reachable-n(H, n0, r, r0) ⊦ r = null, r ≠ null ∧ r ∈ H ∧ (∃ n. reachable-n(H, n, r, r0)), ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null

Rule argument

[var-arg: n0]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : nat generated by 0, +1;], [CSIMPSEQ : ⊦ reachable-n(H, 0, r, r0) ↔ r = r0], [CSIMPSEQ : ⊦ H[r] .nxt = null → ( reachable(r, r0, H) ↔ ¬ ¬ ( r ∈ H ∧ r ≠ null ∧ r = r0))])]]