| # lpt1 = # avol, # lpt2 = # avol, pstate = readonly ↔ isbuf0, isbuf ↔ isbuf0, adr = adr3, adr0 = adr2, adr1 = adr3, keyset(gch) = gc-heap(lpt2, log1), log = log1, log0 = log1, log2 = log1, lpt = lpt1, lpt0 = lpt2, m0 = m2, maxino = m, ns = ns4, ns0 = ns1, ns1 = ns2, ns3 = ns4, 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, lpt2, gstore, ginval), abs-istore(avol, lpt2, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(pstate = readonly, bleb, lpt2, avol), bufs-log-only(bleb, log1, lpt2), flash-lpt-cons(lpt1, istore0, gstore0), freelist-cons(lpt2, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt2), lpt-free-unref(lpt1), lpt-free-unref(lpt2), lpt-leb-size(lpt1), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt1, log1), synced(avol), istore0 ⊑ istore, 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 ⊦ [awbuf_destroy_buf#(adr, m, log, avol, lpt, ns, isbuf; bleb; err); if err = ESUCCESS then awbuf_commit#(lpt0, adr0, m0, avol, bleb; ns0, adr, m, log, lpt, ns, isbuf; err); if err = ESUCCESS then {persistence_gc_heap_add_log#(; log0, lpt0, gch); persistence_cleanup_lpt#(adr, m, log, lpt, ns, bleb, isbuf; lpt0, freelist, gch, avol)}] ( lpt-free-unref(lpt0) ∧ lpt-free-unref(lpt) ∧ freelist-cons(lpt0, freelist) ∧ log0 = log ∧ bin-heap-inv(gch, lpt0) ∧ keyset(gch) = gc-heap(lpt0, log) ∧ bufs-log-only(bleb, log, lpt0) ∧ # lpt0 = # avol ∧ ¬ dups(log) ∧ log-group-block(log, lpt0) ∧ buf-ro-rw-mode(isbuf, bleb, lpt0, avol) ∧ lpt-leb-size(lpt0) ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt0, lpt, log) ∧ awbuf-inv(avol, bleb) ∧ # lpt = # avol ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → bleb = nobuffer) ∧ (err = ESUCCESS ↔ ¬ isbuf) → ⟨apersistence_commit#(adr2, m2, true; ns2, istore, ginval, gstore, adr1, istore0, gstore0, log2, maxino, ns3; pstate, err0)⟩ ( abs-istore(avol, lpt0, istore) ∧ abs-gstore(avol, lpt0, gstore, ginval) ∧ adr1 = adr ∧ maxino = m ∧ log2 = log ∧ ginval < # lpt0 ∧ ns3 = ns ∧ flash-lpt-cons(lpt, istore0, gstore0) ∧ synced(avol) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ isbuf) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ ns0 = ns2 ∧ err = err0)), dups(log1) |
# lpt2 = # avol, # lpt1 = # avol, keyset(gch) = gc-heap(lpt2, log1), 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, lpt2, gstore, ginval), abs-istore(avol, lpt2, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(pstate = readonly, bleb, lpt2, avol), bufs-log-only(bleb, log1, lpt2), flash-lpt-cons(lpt1, istore0, gstore0), freelist-cons(lpt2, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt1), lpt-leb-size(lpt2), lpt-leb-size(lpt1), lpt-ram-flash(lpt2, lpt1, log1), synced(avol), istore0 ⊑ istore, ¬ dups(log1), 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 ⊦ [awbuf_destroy_buf#(adr3, m, log1, avol, lpt1, ns4, pstate = readonly; bleb; err); ns0 := ns2; ns := ns4; maxino := m; log := log1; adr := adr3; isbuf0 := pstate = readonly; if err = ESUCCESS then awbuf_commit#(lpt2, adr2, m2, avol, bleb; ns0, adr, m, log, lpt1, ns, isbuf0; err); log0 := log1; if err = ESUCCESS then {persistence_gc_heap_add_log#(; log0, lpt2, gch); persistence_cleanup_lpt#(adr, m, log, lpt1, ns, bleb, isbuf0; lpt2, freelist, gch, avol)}] ( lpt-free-unref(lpt2) ∧ lpt-free-unref(lpt1) ∧ freelist-cons(lpt2, freelist) ∧ log0 = log ∧ bin-heap-inv(gch, lpt2) ∧ keyset(gch) = gc-heap(lpt2, log) ∧ bufs-log-only(bleb, log, lpt2) ∧ # lpt2 = # avol ∧ ¬ dups(log) ∧ log-group-block(log, lpt2) ∧ buf-ro-rw-mode(isbuf0, bleb, lpt2, avol) ∧ lpt-leb-size(lpt2) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt2, lpt1, log) ∧ awbuf-inv(avol, bleb) ∧ # lpt1 = # avol ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → bleb = nobuffer) ∧ (err = ESUCCESS ↔ ¬ isbuf0) → ⟨apersistence_commit#(adr2, m2, true; ns2, istore, ginval, gstore, adr3, istore0, gstore0, log1, maxino, ns4; pstate, err0)⟩ ( abs-istore(avol, lpt2, istore) ∧ abs-gstore(avol, lpt2, gstore, ginval) ∧ adr3 = adr ∧ maxino = m ∧ log1 = log ∧ ginval < # lpt2 ∧ ns4 = ns ∧ flash-lpt-cons(lpt1, istore0, gstore0) ∧ synced(avol) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ isbuf0) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ ns0 = ns2 ∧ err = err0))