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Proof step 80 from proof inv-allocate-gnd (previous step)

# 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), ( buffered(n0) = nobuffer ∨ buffered(n0).leb < # lpt[n0, mklp(0, 0, LP_GROUP_NODES, m2)] ∧ ( log1 + n0 ' ≠ [] ∧ buffered(n0).leb = (log1 + n0 ').last ∧ lpt[n0, mklp(0, 0, LP_GROUP_NODES, m2)][buffered(n0).leb].flags = LP_GROUP_NODES ∨ lpt[n0, mklp(0, 0, LP_GROUP_NODES, m2)][buffered(n0).leb].flags = LP_INDEX_NODES)) ∧ ¬ n0 ∈ log1 ∧ log-group-block(log1 + n0 ', lpt[n0, mklp(0, 0, LP_GROUP_NODES, m2)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 81:
# 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 ∧ log-group-block(log1 + n0 ', lpt[n0, mklp(0, 0, LP_GROUP_NODES, m2)])

Rule argument

Additional information

Used simplifier rules: ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ m < # lpt → lpt[m, lp][m] = lp; (s)% ⊦ (nx + n ').last = n; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ nx + n ' ≠ []; (s)% ⊦ # lpt[n, lp] = # lpt; (s)% ⊦ buffered(m).leb = m; (s)% ⊦ nobuffer ≠ buffered(m); (s)