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Proof step 51 from proof reach-n-path-n (previous step)

⊦ path(x, H) ↔ # x = 1 ∧ hd x ∈ H ∧ hd x ≠ null ∨ # x = 1 + 1 ∧ hd x ∈ H ∧ hd tl x ∈ H ∧ hd x ≠ null ∧ hd tl x ≠ null ∧ H[hd x].nxt = hd tl x ∨ # x ≥ 1 + 1 ∧ hd x ∈ H ∧ hd x ≠ null ∧ H[hd x].nxt = hd tl x ∧ path(tl x, H)

Lemma k-path