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Proof step 9 from proof fromnext-reachable (previous step)

path(r ' + x, H), x.last ∈ H ⊦ x = [], r = x.last, ∃ x0. path(H[r].nxt ' + x0, H) ∧ (H[r].nxt ' + x0).last = x.last

User applied rule constructor cut

And obtained the following new goals

Proof step 10:
x = r0 + x1, path(r ' + x, H), x.last ∈ H ⊦ x = [], r = x.last, ∃ x0. path(H[r].nxt ' + x0, H) ∧ (H[r].nxt ' + x0).last = x.last

Rule argument

var: x

Additional information

Used simplifier rules: reflist freely generated by [], +;;