| # lpt0 = # avol, # lpt = # avol, gstore[m] = groupblock(gndx1, lax, m1), lpt[m] = mklp(m1, m2, LP_GROUP_NODES, m3), ax = ax0, gndx = gndx0, keyset(gch) = gc-heap(lpt, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, m < # avol, ginval < # avol, abs-istore(avol, lpt, istore), abs-leb(avol[m], groupblock(gndx1, lax, m1), mklp(m1, m2, LP_GROUP_NODES, m3)), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(groupblock(gndx1, lax, m1)), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), 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), m ∈ gstore, istore0 ⊑ istore, ¬ dups(log1), ¬ m ∈ ginval, pstate = unbuffered → isbuf, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer, isbuf → synced(avol) ⊦ ⟪persistence_read_gblock_nodes#(m, LEB_SIZE, adr0, m0, log1, avol, lpt0, ns0, bleb, pstate = readonly; ax, gndx; err)⟫ ⟨apersistence_read_gblock_nodes#(m, adr0, istore, istore0, ginval, gstore, gstore0, log1, m0, ns0, pstate, isbuf; ax0, gndx0; err0)⟩ ( (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ ax = ax0 ∧ gndx = gndx0 ∧ err = err0) |
lpt-free-unref(lpt), log = log0, bufs-log-only(bleb, log, lpt0), # lpt0 = # avol, buf-ro-rw-mode(isbuf, bleb, lpt0, avol), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log), m = LEB_SIZE, awbuf-inv(avol, bleb), # lpt = # avol, m0 < # avol, avol[m0].mapped?, ∃ gndx, lax. abs-nodes(avol[m0].data, gndx, lax, true), ax = ax0, gndx0 = gndx1 ⊦ ⟪persistence_read_gblock_nodes#(m0, m, adr, m1, log0, avol, lpt, ns, bleb, isbuf; ax0, gndx1; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → (∃ lax, gndx. ax0 = ax + lax.to-adr(m0) ∧ gndx1 = gndx0 + gndx ∧ abs-nodes(avol[m0].data, gndx, lax, true))))
# lpt = # avol, # lpt0 = # avol, lpt[m] = mklp(m1, m2, LP_GROUP_NODES, m3), gstore[m] = groupblock(gndx1, lax, m1), ax = ax0, gndx = gndx0, keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, m < # avol, abs-istore(avol, lpt, istore), abs-leb(avol[m], groupblock(gndx1, lax, m1), mklp(m1, m2, LP_GROUP_NODES, m3)), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), inv(groupblock(gndx1, lax, m1)), 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), m ∈ gstore, istore0 ⊑ istore, isbuf → synced(avol), pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate = unbuffered → isbuf ⊦ dups(log1), m ∈ ginval, lpt-free-unref(lpt0) ∧ log1 = log1 ∧ bufs-log-only(bleb, log1, lpt) ∧ # lpt = # avol ∧ buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol) ∧ lpt-leb-size(lpt0) ∧ lpt-ram-flash(lpt, lpt0, log1) ∧ LEB_SIZE = LEB_SIZE ∧ awbuf-inv(avol, bleb) ∧ # lpt0 = # avol ∧ m < # avol ∧ avol[m].mapped? ∧ (∃ gndx, lax. abs-nodes(avol[m].data, gndx, lax, true)) ∧ ax = ax ∧ gndx = gndx
# lpt = # avol, # lpt0 = # avol, isbuf0 ↔ pstate = readonly, LEB_SIZE = LEB_SIZE, lpt[m] = mklp(m1, m2, LP_GROUP_NODES, m3), gstore[m] = groupblock(gndx1, lax, m1), adr1 = adr0, avol0 = avol, ax = ax0, ax = ax, ax1 = ax, bleb0 = bleb, gndx = gndx0, gndx = gndx, gndx2 = gndx, keyset(gch) = gc-heap(lpt, log1), log1 = log1, log2 = log1, log3 = log1, lpt1 = lpt0, lpt2 = lpt, m4 = LEB_SIZE, m5 = m, m6 = m0, ns1 = ns0, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, avol[m].mapped?, ginval < # avol, m < # avol, abs-istore(avol, lpt, istore), abs-leb(avol[m], groupblock(gndx1, lax, m1), mklp(m1, m2, LP_GROUP_NODES, m3)), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), inv(groupblock(gndx1, lax, m1)), 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), m ∈ gstore, istore0 ⊑ istore, isbuf → synced(avol), pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate = unbuffered → isbuf, ∃ gndx, lax. abs-nodes(avol[m].data, gndx, lax, true) ⊦ [persistence_read_gblock_nodes#(m, LEB_SIZE, adr0, m0, log1, avol, lpt0, ns0, bleb, pstate = readonly; ax, gndx; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → (∃ lax, gndx3. ax = ax1 + lax.to-adr(m5) ∧ gndx = gndx2 + gndx3 ∧ abs-nodes(avol0[m5].data, gndx3, lax, true))) → ⟨apersistence_read_gblock_nodes#(m, adr0, istore, istore0, ginval, gstore, gstore0, log1, m0, ns0, pstate, isbuf; ax0, gndx0; err0)⟩ ( (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ ax = ax0 ∧ gndx = gndx0 ∧ err = err0)), dups(log1), m ∈ ginval