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Proof step 87 from proof rem-stays-reachable-aux (previous step)

ce.nxt = H[H[r0].nxt].nxt, path(H[r0, ce][H[r0].nxt].nxt ' + x + H[r0].nxt ', H[r0, ce]), path(r ' + x2 + r0 ', H), path(r ' + x2 + r0 ', H[r0, ce]), H[r0].nxt ∈ H[r0, ce], r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = null, H[r0].nxt = ce.nxt, r = r0, r0 = H[r0, ce][H[r0].nxt].nxt, r0 = null, dups(x2), path(r ' + x2 + r0 ' + (H[r0, ce][H[r0].nxt].nxt ' + x) + H[r0].nxt ', H[r0, ce]), r0 ∈ x, r ∈ x2, r0 ∈ x2, path(ce.nxt ' + x + H[r0].nxt ', H[r0, ce]) ∧ ce.nxt = H[r0, ce][H[r0].nxt].nxt

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: linheap name: At-other seq: ⊦ r ≠ r0 → H[r0, ce][r] = H[r] subst: [r, ce, r0, H] → [H[r0].nxt, ce, r0, H] flags: <all paths>

Additional information

Used simplifier rules: ⊦ r ≠ r0 → (r ∈ H[r0, ce] ↔ r ∈ H); (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r = r0 → H[r0, ce][r] = ce; (s) Used terms: H[r0].nxt, ce, r0, H