| # lpt1 = # avol, lpt1[m] = mklp(m0, m1, LP_GROUP_NODES, m2), bh1 = gch, keyset(gch) = gc-heap(lpt1, log), lpt = lpt1[m, mklp(n, m1, LP_GROUP_NODES, m2)], # gc-heap(lpt1, log) ≠ 0, gc-heap(lpt1, log) ≠ ∅, m < # avol, bin-heap-inv(gch, lpt1), buf-ro-rw-mode(isbuf, bleb, lpt1, avol), bufs-log-only(bleb, log, lpt1), freelist-cons(lpt1, freelist), log-group-block(log, lpt1), lpt-free-unref(lpt1), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log), key-index(m0, m) ∈ gc-heap(lpt1, log), ¬ dups(log), ¬ m ∈ log ⊦ [gc_heap_update#(lpt[m].gcheapidx, n; gch, lpt)] ( bin-heap-inv(gch, lpt) ∧ id-idx(lpt1[m, mklp(n, m1, LP_GROUP_NODES, m2)], lpt) ∧ keyset(gch) = (keyset(bh1) -- key-index(m0, m)) ++ key-index(n, m) → keyset(gch) = gc-heap(lpt1[m, mklp(n, m1, LP_GROUP_NODES, m2)], log) ∧ # lpt = # avol ∧ log-group-block(log, lpt) ∧ m1 ≤ LEB_SIZE ∧ lpt-ram-flash(lpt, lpt0, log)) |
# lpt1 = # avol, lpt1[m] = mklp(m0, m1, LP_GROUP_NODES, m2), bh1 = gch, keyset(gch) = gc-heap(lpt1, log), lpt = lpt1[m, mklp(n, m1, LP_GROUP_NODES, m2)], m < # avol, bin-heap-inv(gch, lpt1), buf-ro-rw-mode(isbuf, bleb, lpt1, avol), bufs-log-only(bleb, log, lpt1), freelist-cons(lpt1, freelist), log-group-block(log, lpt1), lpt-free-unref(lpt1), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log), key-index(m0, m) ∈ gc-heap(lpt1, log) ⊦ # gc-heap(lpt1, log) = 0, gc-heap(lpt1, log) = ∅, dups(log), m ∈ log, ∀ gch, lpt. bin-heap-inv(gch, lpt) ∧ id-idx(lpt1[m, mklp(n, m1, LP_GROUP_NODES, m2)], lpt) ∧ keyset(gch) = (keyset(bh1) -- key-index(m0, m)) ++ key-index(n, m) → keyset(gch) = gc-heap(lpt1[m, mklp(n, m1, LP_GROUP_NODES, m2)], log) ∧ # lpt = # avol ∧ log-group-block(log, lpt) ∧ m1 ≤ LEB_SIZE ∧ lpt-ram-flash(lpt, lpt0, log)