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Proof step 88 from proof reachable-addnew-rev (previous step)

r1 = H[r0].nxt, reachable(ce.nxt, r1, H[H[r0].nxt, ce]), reachable(r, r0, H[H[r0].nxt, ce]), reachable(r, r0, H), r ∈ H, r0 ∈ H, r0 ∈ H[H[r0].nxt, ce], r1 ∈ H[H[r0].nxt, ce] ⊦ H[r0].nxt = null, reachable(r, r1, H[H[r0].nxt, ce]), reachable(r, r1, H), H[r0].nxt ∈ H, reachable(r0, r1, H[H[r0].nxt, ce])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 89:
r0 ∈ H[H[r0].nxt, ce], r0 ∈ H, r ∈ H, reachable(r, r0, H), reachable(r, r0, H[H[r0].nxt, ce]), reachable(ce.nxt, H[r0].nxt, H[H[r0].nxt, ce]) ⊦ H[r0].nxt = null, reachable(r0, H[r0].nxt, H[H[r0].nxt, ce]), H[r0].nxt ∈ H, reachable(r, H[r0].nxt, H[H[r0].nxt, ce])

Rule argument

Additional information

Used simplifier rules: reach-reachnext: ⊦ reachable(r, r1, H) → (¬ reachable(r, H[r1].nxt, H) ↔ H[r1].nxt = null ∨ ¬ H[r1].nxt ∈ H);%reach-alloc: ⊦ reachable(r, r1, H) → r1 ∈ H;%In-insert: ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; from specification store[linheap]