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Proof step 2 from proof path-modify-strong (previous step)

r0 ∈ H ⊦ path(x + r1 ', H[r0, ce]) ↔ path(x + r1 ', H), r0 ∈ x

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ r0, H, r1, ce. r0 ∈ H → (path(x0 + r1 ', H[r0, ce]) ↔ path(x0 + r1 ', H)) ∨ r0 ∈ x0, r0 ∈ H ⊦ path((r + x0) + r1 ', H[r0, ce]) ↔ path((r + x0) + r1 ', H), r0 ∈ r + x0

Rule argument

indvar: x

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null);%reflist freely generated by [], +;;%Nil: ⊦ [] + x0 = x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%In-insert: ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; from specification store[linheap]%in-empty: ⊦ ¬ r ∈ []; from specification list[reflist]