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Proof step 43 from proof inv-commit (previous step)

# lpt0 = # avol, # lpt2 = # avol, keyset(gch) = gc-heap(lpt2, log1), lpt1 = lpt2, awbuf-inv(avol, bleb0), awbuf-inv(avol, nobuffer), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb0, lpt2, avol), bufs-log-only(bleb0, log1, lpt2), freelist-cons(lpt2, freelist), log-group-block(log1, lpt2), lpt-free-unref(lpt0), lpt-free-unref(lpt2), lpt-leb-size(lpt0), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt0, log1), synced(avol), ¬ dups(log1) ⊦ ⟪persistence_gc_heap_add_log#(; log1, lpt2, gch); persistence_cleanup_lpt#(adr0, m0, [], lpt1, ns0, nobuffer, false; lpt2, freelist, gch, avol)⟫ ( lpt-free-unref(lpt2) ∧ lpt-free-unref(lpt1) ∧ freelist-cons(lpt2, freelist) ∧ log1 = [] ∧ bin-heap-inv(gch, lpt2) ∧ keyset(gch) = gc-heap(lpt2, []) ∧ # lpt2 = # avol ∧ lpt-leb-size(lpt2) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt2, lpt1, []) ∧ awbuf-inv(avol, nobuffer) ∧ # lpt1 = # avol)

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: prepost-gcheap-add-log seq: bin-heap-inv(gch, lpt), keyset(gch) = gc-heap(lpt, nx), lpt0 = lpt, ¬ dups(nx), ∀ n. n ∈ nx → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ⊦ ⟪persistence_gc_heap_add_log#(; nx, lpt, gch)⟫ ( nx = [] ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, nx) ∧ id-idx(lpt0, lpt)) subst: [gch, lpt, nx, lpt0] → [gch, lpt2, log1, lpt2] flags: <all paths>

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