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Proof step 9 from proof reachable-addnewtonull-rev (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 10:
∀ ce, r, H, r2. ce.nxt = null ∧ path(r ' + x0, H[r2, ce]) ∧ (r ' + x0).last ∈ H ∧ (r ' + x0).last ∈ H[r2, ce] → r2 ∈ H ∨ path(r ' + x0, H), ce.nxt = null, path(r ' + (r0 + x0), H[r2, ce]), (r ' + (r0 + x0)).last ∈ H, (r ' + (r0 + x0)).last ∈ H[r2, ce] ⊦ r2 ∈ H, path(r ' + (r0 + x0), H)

Rule argument

indvar: x

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null);%reflist freely generated by [], +;;%app: ⊦ x0 + [] = x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%l: ⊦ r '.last = r; from specification list-last[reflist]