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Proof step 13 from proof k-reachable-def (previous step)

path(H[r].nxt ' + x0, H), r ∈ H, ∀ r, H. path(r ' + x0, H) → x0 = [] ∨ r = null ∨ (∃ n. reachable-n(H, n, r, x0.last)) ⊦ r = null, ∃ n. reachable-n(H, n, r, (H[r].nxt ' + x0).last)

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 14:
x0 = [], path(H[r].nxt ' + x0, H), r ∈ H, ∀ r, H. path(r ' + x0, H) → x0 = [] ∨ r = null ∨ (∃ n. reachable-n(H, n, r, x0.last)) ⊦ r = null, ∃ n. reachable-n(H, n, r, (H[r].nxt ' + x0).last)
Proof step 16:
path(H[r].nxt ' + x0, H), r ∈ H, ∀ r, H. path(r ' + x0, H) → x0 = [] ∨ r = null ∨ (∃ n. reachable-n(H, n, r, x0.last)) ⊦ x0 = [], r = null, ∃ n. reachable-n(H, n, r, (H[r].nxt ' + x0).last)

Rule argument

fma: x0 = []

Additional information

Used formulas: x0 = []