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Proof step 55 from proof refine-sync (previous step)

# lpt0 = # avol, # lpt = # avol, pstate = readonly ↔ isbuf0, lpt[bleb.leb] = mklp(m0, m1, lpf, m2), 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(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), 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, bleb.isbuf? ∧ pstate ≠ readonly → bleb.leb < # avol ∧ # avol[bleb.leb].data ≤ LEB_SIZE ∧ avol[bleb.leb].mapped? ∧ m1 = # avol[bleb.leb].data ∧ lpf ≠ LP_FREE ∧ is-aligned(# avol[bleb.leb].data, 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, freelist) ∧ 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-ram-flash(lpt, lpt0, log1) ∧ awbuf-inv(avol, bleb) ∧ # lpt0 = # 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))

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 56:
# lpt = # avol, # lpt0 = # avol, pstate = readonly ↔ isbuf0, lpt[bleb.leb] = mklp(m0, m1, lpf, m4), adr = adr0, bleb0 = bleb, keyset(gch) = gc-heap(lpt, log1), log = log1, m2 = m, m3 = LEB_SIZE, ns = 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), 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, bleb.isbuf? ∧ pstate ≠ readonly → bleb.leb < # avol ∧ # avol[bleb.leb].data ≤ LEB_SIZE ∧ avol[bleb.leb].mapped? ∧ m1 = # avol[bleb.leb].data ∧ lpf ≠ LP_FREE ∧ is-aligned(# avol[bleb.leb].data, 2 * NODE_HEADER_SIZE), 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) ⊦ [if bleb0.isbuf? ∧ ¬ isbuf0 → bleb0.leb < # lpt ∧ lpt[bleb0.leb].size ≤ LEB_SIZE ∧ avol[bleb0.leb].mapped? ∧ lpt[bleb0.leb].size = # avol[bleb0.leb].data ∧ lpt[bleb0.leb].flags ≠ LP_FREE ∧ is-aligned(lpt[bleb0.leb].size, 2 * NODE_HEADER_SIZE) then {err := ESUCCESS; let bleb = ?, isbuf = ?, m1 = ? in {awbuf_get_buf#(adr, m2, log, avol, lpt0, ns, bleb0, isbuf0; ; bleb); awbuf_is_readonly#(adr, m2, log, avol, lpt0, ns, bleb0, isbuf0; ; isbuf); awbuf_get_page_size#(adr, m2, log, avol, lpt0, ns, bleb0, isbuf0; ; m1); if ¬ isbuf then if bleb.isbuf? then let m0 = lpt[bleb.leb].size in if ¬ is-aligned(m0, m1) then let m = m1 - m0 % m1 in let buf = mkbuf(m) in {persistence_encode_padding_node#(; buf; err); if err = ESUCCESS then {awbuf_write_buf#(# buf, buf, adr, m2, log, lpt0, ns, bleb0; avol, isbuf0; err); if err = ESUCCESS then lpt[bleb.leb].size := lpt[bleb.leb].size + m else {debug#("persistence: flushing of LEB " + bleb.leb.toString + " failed"); lpt[bleb.leb].size := m3; awbuf_enter_readonly#(adr, m2, log, avol, lpt0, ns, bleb0; ; isbuf0)}} else {debug#("persistence: could not encode padding node"); awbuf_enter_readonly#(adr, m2, log, avol, lpt0, ns, bleb0; ; isbuf0)}} else err := EROFS}} else abort] ( lpt-free-unref(lpt) ∧ freelist-cons(lpt, freelist) ∧ 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-ram-flash(lpt, lpt0, log1) ∧ awbuf-inv(avol, bleb) ∧ # lpt0 = # 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)

Rule argument

pos: right 1

Additional information

Used simplifier rules: persistence_sync# (LEBSIZE, WROOTADR, WMAXINO, WLOG, WLPT, WORPHANS, WBUFLEB ; LPT, WVOL, AROFS ; ERR ) {if WBUFLEB.isbuf? ∧ ¬ AROFS → WBUFLEB.leb < # LPT ∧ LPT[WBUFLEB.leb].size ≤ LEB_SIZE ∧ WVOL[WBUFLEB.leb].mapped? ∧ LPT[WBUFLEB.leb].size = # WVOL[WBUFLEB.leb].data ∧ LPT[WBUFLEB.leb].flags ≠ LP_FREE ∧ is-aligned(LPT[WBUFLEB.leb].size, 2 * NODE_HEADER_SIZE) then {ERR := ESUCCESS; let WBUFLEB0 = ?, AROFS0 = ?, PAGESIZE = ? in {awbuf_get_buf# (WROOTADR, WMAXINO, WLOG, WVOL, WLPT, WORPHANS, WBUFLEB, AROFS ; ; WBUFLEB0); awbuf_is_readonly# (WROOTADR, WMAXINO, WLOG, WVOL, WLPT, WORPHANS, WBUFLEB, AROFS ; ; AROFS0); awbuf_get_page_size# (WROOTADR, WMAXINO, WLOG, WVOL, WLPT, WORPHANS, WBUFLEB, AROFS ; ; PAGESIZE); if ¬ AROFS0 then if WBUFLEB0.isbuf? then let OFFSET = LPT[WBUFLEB0.leb].size in if ¬ is-aligned(OFFSET, PAGESIZE) then let SIZE = PAGESIZE - OFFSET % PAGESIZE in let BUF = mkbuf(SIZE) in {persistence_encode_padding_node# (; BUF; ERR); if ERR = ESUCCESS then {awbuf_write_buf# (# BUF, BUF, WROOTADR, WMAXINO, WLOG, WLPT, WORPHANS, WBUFLEB ; WVOL, AROFS ; ERR); if ERR = ESUCCESS then LPT[WBUFLEB0.leb].size := LPT[WBUFLEB0.leb] .size + SIZE else {debug# ( "persistence: flushing of LEB " + WBUFLEB0.leb .toString + " failed"); LPT[WBUFLEB0.leb].size := LEBSIZE; awbuf_enter_readonly# (WROOTADR, WMAXINO, WLOG, WVOL, WLPT, WORPHANS, WBUFLEB ; ; AROFS)}} else {debug# ("persistence: could not encode padding node"); awbuf_enter_readonly# (WROOTADR, WMAXINO, WLOG, WVOL, WLPT, WORPHANS, WBUFLEB ; ; AROFS)}} else ERR := EROFS}} else abort };