| # lpt = # avol, # lpt0 = # avol, pstate = readonly ↔ isbuf0, adr = adr0, adr1 = adr2, keyset(gch) = gc-heap(lpt, log1), keyset(gch) = gc-heap(lpt, log0), log = log1, log0 = log1, m1 = m2, maxino = m, ns = ns0, ns1 = ns2, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom remove-refsize0(gstore) ∩ 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), bufs-log-only(bleb, log0, 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), log-group-block(log0, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log1), lpt-ram-flash(lpt, lpt0, log0), synced(avol), istore0 ⊑ istore, 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 ⊦ [persistence_commit#(adr2, m2; ns1, log0, lpt, freelist, gch, adr0, m, log1, avol, lpt0, ns0, bleb, isbuf0; err)] ( lpt-free-unref(lpt) ∧ lpt-free-unref(lpt0) ∧ freelist-cons(lpt, freelist) ∧ log0 = log1 ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log0) ∧ bufs-log-only(bleb, log0, lpt) ∧ # lpt = # avol ∧ ¬ dups(log0) ∧ log-group-block(log0, lpt) ∧ buf-ro-rw-mode(isbuf0, bleb, lpt, avol) ∧ lpt-leb-size(lpt) ∧ lpt-leb-size(lpt0) ∧ lpt-ram-flash(lpt, lpt0, log0) ∧ awbuf-inv(avol, bleb) ∧ # lpt0 = # avol ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → bleb = nobuffer) ∧ (err = ESUCCESS ↔ ¬ isbuf0) → ⟨apersistence_commit#(adr2, m2, true; ns2, istore, ginval, gstore, adr, istore0, gstore0, log, maxino, ns; pstate, err0)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ adr = adr0 ∧ maxino = m ∧ log = log0 ∧ ginval < # lpt ∧ ns = ns0 ∧ flash-lpt-cons(lpt0, istore0, gstore0) ∧ synced(avol) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ isbuf0) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ ns1 = ns2 ∧ err = err0)), dups(log0), dups(log1) |
# lpt0 = # avol, # lpt = # avol, pstate = readonly ↔ isbuf0, adr = adr0, keyset(gch) = gc-heap(lpt, log1), log = log1, log0 = log1, maxino = m, ns = ns0, ns1 = ns2, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, dom remove-refsize0(gstore) ∩ ginval = ∅, 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(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log1), synced(avol), istore0 ⊑ istore, ¬ dups(log1), 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 ⊦ [persistence_commit#(adr2, m2; ns1, log0, lpt, freelist, gch, adr0, m, log1, avol, lpt0, ns0, bleb, isbuf0; err)] ( lpt-free-unref(lpt) ∧ lpt-free-unref(lpt0) ∧ freelist-cons(lpt, freelist) ∧ log0 = log1 ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log1) ∧ bufs-log-only(bleb, log1, lpt) ∧ # lpt = # avol ∧ ¬ dups(log1) ∧ 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) ∧ awbuf-inv(avol, bleb) ∧ # lpt0 = # avol ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → bleb = nobuffer) ∧ (err = ESUCCESS ↔ ¬ isbuf0) → ⟨apersistence_commit#(adr2, m2, true; ns2, istore, ginval, gstore, adr, istore0, gstore0, log, maxino, ns; pstate, err0)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ adr = adr0 ∧ maxino = m ∧ log = log1 ∧ ginval < # lpt ∧ ns = ns0 ∧ flash-lpt-cons(lpt0, istore0, gstore0) ∧ synced(avol) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ isbuf0) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ ns1 = ns2 ∧ err = err0))