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Proof step 52 from proof inv-deallocate-gnd (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
# 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, awbuf-inv(avol, bleb), bin-heap-inv(gch0, lpt), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb, lpt2, avol), bufs-log-only(bleb, 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, bleb = nobuffer, buffered(n) = bleb, gc-heap(lpt2, log0) = ∅, dups(log0), n ∈ log0, bleb.leb < # avol ∧ (log0 ≠ [] ∧ bleb.leb = log0.last ∧ lpt2[bleb.leb].flags = LP_GROUP_NODES ∨ lpt2[n, mklp(0, 0, LP_FREE, m2)][bleb.leb].flags = LP_INDEX_NODES)

Rule argument

Additional information

Used simplifier rules: m ≠ n ⊦ lpt[m, lp][n] = lpt[n]; (s)% ⊦ nx.last ∈ nx ↔ nx ≠ []; (s)% ⊦ # lpt[n, lp] = # lpt; (s)