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Proof step 83 from proof rem-stays-reachable-aux (previous step)

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

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: rewrite

Additional information

Used simplifier rules: in-neq: ⊦ r ≠ r0 → (r ∈ H[r0, ce] ↔ r ∈ H); from specification store[linheap]%k-At-same: ⊦ r = r0 → H[r0, ce][r] = ce; from specification store[linheap] Used terms: H[r0].nxt, ce, r0, H