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Proof step 59 from proof refine-sync (previous step)

# lpt0 = # avol, # lpt = # avol, pstate = readonly ↔ isbuf0, lpt[bleb1.leb] = mklp(m0, m5, lpf, m4), adr = adr0, bleb0 = bleb1, keyset(gch) = gc-heap(lpt, log1), log = log1, m2 = m, m3 = LEB_SIZE, ns = ns0, 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, bleb1), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb1, lpt, avol), bufs-log-only(bleb1, 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, isbuf1 → synced(avol), pstate = unbuffered → bleb1 = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb1 = buffered(pstate.lnum), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate = unbuffered → isbuf1, bleb1.isbuf? ∧ pstate ≠ readonly → bleb1.leb < # avol ∧ # avol[bleb1.leb].data ≤ LEB_SIZE ∧ avol[bleb1.leb].mapped? ∧ m5 = # avol[bleb1.leb].data ∧ lpf ≠ LP_FREE ∧ is-aligned(# avol[bleb1.leb].data, 2 * NODE_HEADER_SIZE) ⊦ [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); err := ESUCCESS; 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] ( lpt-free-unref(lpt) ∧ freelist-cons(lpt, freelist) ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log1) ∧ bufs-log-only(bleb1, log1, lpt) ∧ # lpt = # avol ∧ log-group-block(log1, lpt) ∧ buf-ro-rw-mode(isbuf0, bleb1, lpt, avol) ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt, lpt0, log1) ∧ awbuf-inv(avol, bleb1) ∧ # lpt0 = # avol → ⟨apersistence_sync#(adr0, istore, istore0, ginval, gstore, gstore0, log1, m, ns0; pstate, isbuf1; err0)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ ginval < # lpt ∧ (isbuf1 → synced(avol)) ∧ (pstate = unbuffered → bleb1 = nobuffer) ∧ (pstate = readonly ↔ isbuf0) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb1 = buffered(pstate.lnum)) ∧ err = err0)), dups(log1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 60:
# lpt = # avol, # lpt0 = # avol, lpt[bleb1.leb] = mklp(m0, m5, lpf, m4), 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, bleb1), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb1, lpt, avol), bufs-log-only(bleb1, 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, ¬ dups(log1), bleb1.isbuf? ∧ pstate ≠ readonly → bleb1.leb < # avol ∧ # avol[bleb1.leb].data ≤ LEB_SIZE ∧ avol[bleb1.leb].mapped? ∧ m5 = # avol[bleb1.leb].data ∧ lpf ≠ LP_FREE ∧ is-aligned(# avol[bleb1.leb].data, 2 * NODE_HEADER_SIZE), pstate = unbuffered → isbuf1, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb1 = buffered(pstate.lnum), pstate = unbuffered → bleb1 = nobuffer, isbuf1 → synced(avol) ⊦ [awbuf_get_buf#(adr0, m, log1, avol, lpt0, ns0, bleb1, pstate = readonly; ; bleb); awbuf_is_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb1, pstate = readonly; ; isbuf); awbuf_get_page_size#(adr0, m, log1, avol, lpt0, ns0, bleb1, pstate = readonly; ; m1); err := ESUCCESS; isbuf0 := pstate = readonly; if ¬ isbuf then if bleb.isbuf? then let m0 = lpt[bleb.leb].size in if ¬ is-aligned(m0, m1) then let m3 = m1 - m0 % m1 in let buf = mkbuf(m3) in {persistence_encode_padding_node#(; buf; err); if err = ESUCCESS then {awbuf_write_buf#(# buf, buf, adr0, m, log1, lpt0, ns0, bleb1; avol, isbuf0; err); if err = ESUCCESS then lpt[bleb.leb] := mklp(lpt[bleb.leb].ref-size, lpt[bleb.leb].size + m3, lpt[bleb.leb].flags, lpt[bleb.leb].gcheapidx) else {debug#("persistence: flushing of LEB " + bleb.leb.toString + " failed"); lpt[bleb.leb] := mklp(lpt[bleb.leb].ref-size, LEB_SIZE, lpt[bleb.leb].flags, lpt[bleb.leb].gcheapidx); awbuf_enter_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb1; ; isbuf0)}} else {debug#("persistence: could not encode padding node"); awbuf_enter_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb1; ; isbuf0)}} else err := EROFS] ( lpt-free-unref(lpt) ∧ freelist-cons(lpt, freelist) ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log1) ∧ bufs-log-only(bleb1, log1, lpt) ∧ # lpt = # avol ∧ log-group-block(log1, lpt) ∧ buf-ro-rw-mode(isbuf0, bleb1, lpt, avol) ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt, lpt0, log1) ∧ awbuf-inv(avol, bleb1) ∧ # lpt0 = # avol → ⟨apersistence_sync#(adr0, istore, istore0, ginval, gstore, gstore0, log1, m, ns0; pstate, isbuf1; err0)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ ginval < # lpt ∧ (isbuf1 → synced(avol)) ∧ (pstate = unbuffered → bleb1 = nobuffer) ∧ (pstate = readonly ↔ isbuf0) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb1 = buffered(pstate.lnum)) ∧ err = err0))

Rule argument

Additional information

Used simplifier rules: ⊦ lp.size:= n = mklp(lp.ref-size, n, lp.flags, lp.gcheapidx); (s)