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Proof step 11 from proof reachable-addnew (previous step)

path(r ' + x, H), x.last ∈ H ⊦ x = [], r2 ∈ H, path(r ' + x, H[r2, ce])

User applied rule structural induction

And obtained the following new goals

Proof step 12:
∀ r, H, r2, ce. path(r ' + x0, H) ∧ x0.last ∈ H → x0 = [] ∨ r2 ∈ H ∨ path(r ' + x0, H[r2, ce]), path(r ' + (r0 + x0), H), (r0 + x0).last ∈ H ⊦ r0 + x0 = [], r2 ∈ H, path(r ' + (r0 + x0), H[r2, ce])

Rule argument

indvar: x

Additional information

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