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Proof step 25 from proof add-preserves-reachable (previous step)

H[r1].nxt = H[ce.nxt].nxt, (H[r1].nxt ' + x).last = (H[r1].nxt ' + x0).last, r1 ∈ H, path(H[r1].nxt ' + x0, H), ce.nxt ∈ H, (H[r1].nxt ' + x0).last ∈ H, reachable(H[r1].nxt, r1, H), path(H[r1].nxt ' + x, H[r1, ce]), ce.nxt ∈ H[r1, ce] ⊦ ce.nxt = null, r1 = null, H[r1, ce][ce.nxt].nxt = H[r1].nxt, reachable(r1, ce.nxt, H)

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] → [ce.nxt, ce, r1, H] flags: rewrite

Additional information

Used simplifier rules: self-reachable: ⊦ reachable(r, r, H) ↔ ¬ ¬(r ≠ null ∧ r ∈ H);%reachable-notnullinH: ⊦ reachable(r, r1, H) → (¬ r1 ∈ H ↔ false);%At-same: ⊦ H[r, ce][r] = ce; from specification store[linheap]%insin: ⊦ r ∈ H[r, ce]; from specification store[linheap] Used terms: ce.nxt, ce, r1, H