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Proof step 31 from proof legal-noncylic-equiv-reaches-null (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 30:
∀ H, r. legal(H) ∧ r ∈ H → r = null ∨ (∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null) ∨ (∃ r0. reachable-n(H, n0, r, r0)), legal(H), r ∈ H ⊦ r = null, ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null, ∃ r0. reachable-n(H, n0 +1, r, r0)

Rule argument

[VARWITHVARSEQSARG : n, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : nat generated by 0, +1;], [CSIMPSEQ : ⊦ reachable-n(H, 0, r, r0) ↔ r = r0])]]