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Proof step 12 from proof reachable-addnew (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 13:
path(r ' + (r0 + x0), H), ∀ r, H, r2, ce. path(r ' + x0, H) → x0 = [] ∨ path(r ' + x0, H[r2, ce]) ∨ r2 ∈ H ⊦ r0 + x0 = [], path(r ' + (r0 + x0), H[r2, ce]), r2 ∈ H

Rule argument

indvar: x

Additional information

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