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Proof step 19 from proof reachable-modbehind (previous step)

path(H[r].nxt ' + x0, H), reachable((H[r].nxt ' + x0).last, r1, H), r1 ∈ H, (H[r].nxt ' + x0).last ∈ H, r ∈ H, ∀ r2, H0, r3, ce0. path(r2 ' + x0, H0) ∧ reachable((r2 ' + x0).last, r3, H0) → path(r2 ' + x0, H0[r3, ce0]) ∨ reachable(r3, (r2 ' + x0).last, H0) ⊦ r = r1, r = null, path(H[r].nxt ' + x0, H[r1, ce]), reachable(r1, (H[r].nxt ' + x0).last, H)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 6 terms: H[r].nxt, H, r1, ce

Additional information

Used terms: H[r].nxt, H, r1, ce