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Proof step 83 from proof inv-allocate-gnd (previous step)

# lpt = # avol0, # lpt0 = # avol0, lpt[n0] = mklp(0, m3, LP_FREE, m2), keyset(gch) = gc-heap(lpt, log1), n0 < # avol0, awbuf-inv(avol0[n0, mapped(mkbuf(0))], bleb), awbuf-inv(avol0, bleb), awbuf-inv(avol0[n0, mapped(mkbuf(0))], buffered(n0)), bin-heap-inv(gch, lpt), bufs-log-only(bleb, log1, lpt), freelist-cons(lpt, n0 ' + nx0), log-group-block(log1, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log1), synced(avol0[n0, mapped(mkbuf(0))]), synced(avol0), bleb.isbuf? → bleb.leb < # avol0 ∧ lpt[bleb.leb].size = # avol0[bleb.leb].data ⊦ buffered(n0) = bleb, dups(log1), ¬ n0 ∈ log1 ∧ (∀ n. n ∈ log1 + n0 ' → n < # lpt[n0, mklp(0, 0, LP_GROUP_NODES, m2)] ∧ lpt[n0, mklp(0, 0, LP_GROUP_NODES, m2)][n].flags = LP_GROUP_NODES)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 84:
# lpt0 = # avol0, # lpt = # avol0, lpt[n0] = mklp(0, m3, LP_FREE, m2), keyset(gch) = gc-heap(lpt, log1), n0 < # avol0, awbuf-inv(avol0[n0, mapped(mkbuf(0))], buffered(n0)), awbuf-inv(avol0, bleb), awbuf-inv(avol0[n0, mapped(mkbuf(0))], bleb), bin-heap-inv(gch, lpt), bufs-log-only(bleb, log1, lpt), freelist-cons(lpt, n0 ' + nx0), log-group-block(log1, lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log1), synced(avol0), synced(avol0[n0, mapped(mkbuf(0))]), bleb.isbuf? → bleb.leb < # avol0 ∧ lpt[bleb.leb].size = # avol0[bleb.leb].data ⊦ buffered(n0) = bleb, dups(log1), ¬ n0 ∈ log1 ∧ (n ∈ log1 ∨ n = n0 → n < # avol0 ∧ lpt[n0, mklp(0, 0, LP_GROUP_NODES, m2)][n].flags = LP_GROUP_NODES)

Rule argument

Additional information

Used simplifier rules: ⊦ # lpt[n, lp] = # lpt; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ n ∈ n0 ' ↔ n = n0; (s)% ⊦ n ∈ nx + nx0 ↔ n ∈ nx ∨ n ∈ nx0; (s)