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Proof step 55 from proof inv-deallocate-gnd (previous step)

# lpt0 = # avol, # lpt2 = # avol, lpt2[n] = mklp(m3, m1, LP_GROUP_NODES, m2), keyset(gch0) = gc-heap(lpt2, log0) -- key-index(m3, n), keyset(gch) = gc-heap(lpt2, log0), n < # avol, m < # avol, awbuf-inv(avol, buffered(m)), bin-heap-inv(gch0, lpt), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, buffered(m), lpt2, avol), bufs-log-only(buffered(m), log0, lpt2), freelist-cons(lpt2, freelist), id-idx(lpt2[n, mklp(0, 0, LP_FREE, m2)], lpt), log-group-block(log0, lpt2[n, mklp(0, 0, LP_FREE, m2)]), log-group-block(log0, lpt2), lpt-free-unref(lpt0), lpt-free-unref(lpt2), lpt-leb-size(lpt0), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt0, log0), synced(avol), key-index(m3, n) ∈ gc-heap(lpt2, log0) ⊦ # gc-heap(lpt2, log0) = 0, lpt2[m].flags = LP_INDEX_NODES, gc-heap(lpt2, log0) = ∅, n = m, dups(log0), n ∈ log0, log0 ≠ [] ∧ m = log0.last ∧ lpt2[log0.last].flags = LP_GROUP_NODES

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: persistence-base name: bufs-log-only seq: ⊦ bufs-log-only(bleb, nx, lpt) ↔ bleb = nobuffer ∨ bleb.leb < # lpt ∧ ( nx ≠ [] ∧ bleb.leb = nx.last ∧ lpt[bleb.leb].flags = LP_GROUP_NODES ∨ lpt[bleb.leb].flags = LP_INDEX_NODES) subst: [lpt, nx, bleb] → [lpt2, log0, buffered(m)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ nobuffer ≠ buffered(m); (s)% ⊦ buffered(m).leb = m; (s) Used terms: lpt2, log0, buffered(m)