| # lpt = # avol, # lpt0 = # avol, pstate = readonly ↔ isbuf0, 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, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), 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), 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), istore0 ⊑ istore, ¬ dups(log1), 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 ⊦ ⟪persistence_sync#(LEB_SIZE, adr0, m, log1, lpt0, ns0, bleb; lpt, avol, isbuf0; err)⟫ ⟨apersistence_sync#(adr0, istore, istore0, ginval, gstore, gstore0, log1, m, ns0; pstate, isbuf; err0)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ ginval < # lpt ∧ (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ isbuf0) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ err = err0) |
lpt-free-unref(lpt), lpt-free-unref(lpt0), freelist-cons(lpt, freelist), log = log0, bin-heap-inv(gch, lpt), keyset(gch) = gc-heap(lpt, log), bufs-log-only(bleb, log, lpt), # lpt = # avol, log-group-block(log, lpt), buf-ro-rw-mode(isbuf, bleb, lpt, avol), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log), m = LEB_SIZE, awbuf-inv(avol, bleb), # lpt0 = # avol, bleb.isbuf? ∧ ¬ isbuf → bleb.leb < # lpt ∧ lpt[bleb.leb].size ≤ LEB_SIZE ∧ avol[bleb.leb].mapped? ∧ lpt[bleb.leb].size = # avol[bleb.leb].data ∧ lpt[bleb.leb].flags ≠ LP_FREE ∧ is-aligned(lpt[bleb.leb].size, 2 * NODE_HEADER_SIZE) ⊦ ⟪persistence_sync#(m, adr, m0, log0, lpt0, ns, bleb; lpt, avol, isbuf; err)⟫ ( lpt-free-unref(lpt) ∧ freelist-cons(lpt, freelist) ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log) ∧ bufs-log-only(bleb, log, lpt) ∧ # lpt = # avol ∧ log-group-block(log, lpt) ∧ buf-ro-rw-mode(isbuf, bleb, lpt, avol) ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt, lpt0, log) ∧ awbuf-inv(avol, bleb) ∧ # lpt0 = # avol)
# lpt0 = # avol, # lpt = # avol, pstate = readonly ↔ isbuf0, keyset(gch) = gc-heap(lpt, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), 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(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), istore0 ⊑ istore, 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) ⊦ dups(log1), lpt-free-unref(lpt) ∧ lpt-free-unref(lpt0) ∧ freelist-cons(lpt, freelist) ∧ log1 = log1 ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log1) ∧ bufs-log-only(bleb, log1, lpt) ∧ # lpt = # avol ∧ log-group-block(log1, lpt) ∧ buf-ro-rw-mode(isbuf0, bleb, lpt, avol) ∧ lpt-leb-size(lpt) ∧ lpt-leb-size(lpt0) ∧ lpt-ram-flash(lpt, lpt0, log1) ∧ LEB_SIZE = LEB_SIZE ∧ awbuf-inv(avol, bleb) ∧ # lpt0 = # avol ∧ ( bleb.isbuf? ∧ ¬ isbuf0 → bleb.leb < # lpt ∧ lpt[bleb.leb].size ≤ LEB_SIZE ∧ avol[bleb.leb].mapped? ∧ lpt[bleb.leb].size = # avol[bleb.leb].data ∧ lpt[bleb.leb].flags ≠ LP_FREE ∧ is-aligned(lpt[bleb.leb].size, 2 * NODE_HEADER_SIZE))
# lpt = # avol, # lpt0 = # avol, pstate = readonly ↔ isbuf0, LEB_SIZE = LEB_SIZE, adr1 = adr0, bleb0 = bleb, freelist0 = freelist, gch0 = gch, keyset(gch) = gc-heap(lpt, log1), log1 = log1, log2 = log1, log3 = log1, lpt1 = lpt0, m1 = LEB_SIZE, m2 = m, ns1 = ns0, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), buf-ro-rw-mode(isbuf0, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), 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), istore0 ⊑ istore, 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), bleb.isbuf? ∧ ¬ isbuf0 → bleb.leb < # lpt ∧ lpt[bleb.leb].size ≤ LEB_SIZE ∧ avol[bleb.leb].mapped? ∧ lpt[bleb.leb].size = # avol[bleb.leb].data ∧ lpt[bleb.leb].flags ≠ LP_FREE ∧ is-aligned(lpt[bleb.leb].size, 2 * NODE_HEADER_SIZE) ⊦ [persistence_sync#(LEB_SIZE, adr0, m, log1, lpt0, ns0, bleb; lpt, avol, isbuf0; err)] ( lpt-free-unref(lpt) ∧ freelist-cons(lpt, freelist0) ∧ bin-heap-inv(gch0, lpt) ∧ keyset(gch0) = gc-heap(lpt, log2) ∧ bufs-log-only(bleb0, log2, lpt) ∧ # lpt = # avol ∧ log-group-block(log2, lpt) ∧ buf-ro-rw-mode(isbuf0, bleb0, lpt, avol) ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt, lpt1, log2) ∧ awbuf-inv(avol, bleb0) ∧ # lpt1 = # avol → ⟨apersistence_sync#(adr0, istore, istore0, ginval, gstore, gstore0, log1, m, ns0; pstate, isbuf; err0)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ ginval < # lpt ∧ (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ isbuf0) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ err = err0)), dups(log1)