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Proof step 8 from proof path-new-irrelevant-strong (previous step)

r ∈ H[r2, ce], path(H[r].nxt ' + x0, H[r2, ce]), r ∈ H, ∀ r, H, r2, ce. r ∈ H → (path(r ' + x0, H[r2, ce]) ↔ path(r ' + x0, H)) ∨ r2 ∈ x0 ∨ r2 ∈ H ⊦ r2 = H[r].nxt, r = null, path(H[r].nxt ' + x0, H), r2 ∈ x0, r2 ∈ H, H[r].nxt ∈ H

User applied rule constructor cut

And closed the goal!

Rule argument

var: x0

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null);%path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H));%reflist freely generated by [], +;;%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%in-neq: ⊦ r ≠ r0 → (r ∈ H[r0, ce] ↔ r ∈ H); from specification store[linheap]%app: ⊦ x0 + [] = x0; from specification list[reflist]