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Proof step 11 from proof k-reachable-def (previous step)

path(r ' + x, H) ⊦ r = null, x = [], ∃ n. reachable-n(H, n, r, x.last)

User applied rule structural induction

And obtained the following new goals

Proof step 12:
path(r ' + (r0 + x0), H), ∀ r, H. path(r ' + x0, H) → r = null ∨ x0 = [] ∨ (∃ n. reachable-n(H, n, r, x0.last)) ⊦ r0 + x0 = [], r = null, ∃ n. reachable-n(H, n, r, (r0 + x0).last)

Rule argument

indvar: x

Additional information

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