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Proof step 6 from proof reachable-nodups-def (previous step)

path(r ' + x, H) ⊦ ∃ x0. path(r ' + x0, H) ∧ (r ' + x0).last = (r ' + x).last ∧ ¬ r ∈ x0 ∧ ¬ dups(x0)

User applied rule structural induction

And obtained the following new goals

Proof step 7:
path(r ' + [], H) ⊦ ∃ x0. path(r ' + x0, H) ∧ (r ' + x0).last = (r ' + []).last ∧ ¬ r ∈ x0 ∧ ¬ dups(x0)
Proof step 9:
∀ r, H. path(r ' + x0, H) → (∃ x1. path(r ' + x1, H) ∧ (r ' + x1).last = (r ' + x0).last ∧ ¬ r ∈ x1 ∧ ¬ dups(x1)), path(r ' + (r0 + x0), H) ⊦ ∃ x1. path(r ' + x1, H) ∧ (r ' + x1).last = (r ' + (r0 + x0)).last ∧ ¬ r ∈ x1 ∧ ¬ dups(x1)

Rule argument

indvar: x

Additional information

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