| # lpt1 = # avol, # lpt0 = # avol, lpt1[m] = mklp(m1, m2, LP_GROUP_NODES, m3), gstore[m] = groupblock(gndx, lax, m1), adr = adr0, istore = istore1, istore0 = istore2, keyset(gch0) = (gc-heap(lpt1, log0) -- key-index(m1, m)) ++ key-index(n, m), keyset(gch) = gc-heap(lpt1, log0), log = log0, maxino = m0, ns = ns0, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, elems log0 ∩ ginval = ∅, dom gstore0 ∪ elems log0 = dom gstore ∪ ginval, m < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), awbuf-inv(avol, bleb), bin-heap-inv(gch0, lpt2), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(pstate = readonly, bleb, lpt1, avol), bufs-log-only(bleb, log0, lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), id-idx(lpt1[m, mklp(n, m2, LP_GROUP_NODES, m3)], lpt2), inv(gstore \ ginval), inv(gstore0), inv(istore2), inv(istore1), log-group-block(log0, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log0), m ∈ gstore0, m ∈ gstore, key-index(m1, m) ∈ gc-heap(lpt1, log0), istore1 ⊑ istore2, isbuf → synced(avol), pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log0 ≠ [] ∧ pstate.lnum = log0.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore2, pstate = unbuffered → isbuf ⊦ ⟨gstore[m].ref-size := n⟩ ( abs-gstore(avol, lpt1[m, mklp(n, m2, LP_GROUP_NODES, m3)], gstore, ginval) ∧ ginval < # lpt2 ∧ (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum))), # gc-heap(lpt1, log0) = 0, gc-heap(lpt1, log0) = ∅, dups(log0), m ∈ log0 |
# lpt0 = # avol, # lpt1 = # avol, gstore[m] = groupblock(gndx, lax, m1), lpt1[m] = mklp(m1, m2, LP_GROUP_NODES, m3), adr = adr0, istore = istore1, istore0 = istore2, keyset(gch) = gc-heap(lpt1, log0), keyset(gch0) = (gc-heap(lpt1, log0) -- key-index(m1, m)) ++ key-index(n, m), log = log0, maxino = m0, ns = ns0, remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, elems log0 ∩ ginval = ∅, dom gstore0 ∪ elems log0 = dom gstore ∪ ginval, ginval < # avol, m < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt1), bin-heap-inv(gch0, lpt2), buf-ro-rw-mode(pstate = readonly, bleb, lpt1, avol), bufs-log-only(bleb, log0, lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), id-idx(lpt1[m, mklp(n, m2, LP_GROUP_NODES, m3)], lpt2), inv(istore1), inv(istore2), inv(gstore0), inv(gstore \ ginval), log-group-block(log0, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log0), key-index(m1, m) ∈ gc-heap(lpt1, log0), m ∈ gstore, m ∈ gstore0, istore1 ⊑ istore2, pstate = unbuffered → isbuf, pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → log0 ≠ [] ∧ pstate.lnum = log0.last ∧ pstate.lnum ∈ gstore, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer, isbuf → synced(avol) ⊦ # gc-heap(lpt1, log0) = 0, gc-heap(lpt1, log0) = ∅, dups(log0), m ∈ log0, abs-gstore(avol, lpt1[m, mklp(n, m2, LP_GROUP_NODES, m3)], gstore[m, gstore[m].ref-size:= n], ginval) ∧ ginval < # lpt2 ∧ (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum))