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Proof step 2 from proof path-prefix (previous step)

path(r ' + x + y, H) ⊦ path(r ' + x, H)

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ r, y, H. path(r ' + x0 + y, H) → path(r ' + x0, H), path(r ' + (r0 + x0) + y, H) ⊦ path(r ' + (r0 + x0), H)

Rule argument

indvar: x

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null);%path-first-in-H: ⊦ path(r ' + x, H) → (¬ r ∈ H ↔ false);%null-not-start-of-path: ⊦ ¬ path(null ' + x, H);%reflist freely generated by [], +;;%Nil: ⊦ [] + x0 = x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%app: ⊦ x0 + [] = x0; from specification list[reflist]