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Proof step 12 from proof reach-n-next-legal (previous step)

r ∈ H, legal(H), reachable-n(H, n, r, r0) ⊦ r = null, (∀ r1. ¬ reachable-n(H, n, r, r1) ∨ ¬ reachable-1(H, r1, H[r0] .nxt)) ↔ H[r0] .nxt = null

User applied rule case distinction

And obtained the following new goals

Proof step 11:
∀ r1. ¬ reachable-n(H, n, r, r1) ∨ ¬ reachable-1(H, r1, H[r0] .nxt), r ∈ H, legal(H), reachable-n(H, n, r, r0) ⊦ H[r0] .nxt = null, r = null

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

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