| # lpt0 = # avol, # lpt1 = # avol, isbuf1 ↔ false, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, lpt1[pstate.lnum] = mklp(m1, # buf0, lpf, m4), avol[pstate.lnum] = mapped(buf0), adr = adr0, bleb = buffered(pstate.lnum), keyset(gch) = gc-heap(lpt1, log1), log = log1, lpt = lpt0, ns = ns0, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, pstate.lnum < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, buffered(pstate.lnum)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt1, avol), buf-ro-rw-mode(true, buffered(pstate.lnum), lpt1, avol), bufs-log-only(buffered(pstate.lnum), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), is-aligned(# buf0, 2 * NODE_HEADER_SIZE), log-group-block(log1, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log1), # buf0 ≤ LEB_SIZE, istore0 ⊑ istore, ⌊err⌋ , pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate.index? ∨ pstate.journal? ⊦ ⟨pstate0 := pstate; apersistence_sync#(adr0, istore, istore0, ginval, gstore, gstore0, log1, m, ns0; pstate, isbuf1; err0)⟩ ( ginval < # lpt1 ∧ (isbuf1 → synced(avol)) ∧ pstate ≠ unbuffered ∧ (pstate = readonly ↔ true) ∧ (pstate ≠ readonly → pstate0.lnum = pstate.lnum) ∧ err = err0), buf1 = mkbuf(0), lpf = LP_FREE, pstate = readonly, pstate = unbuffered, dups(log1), is-aligned(# buf0, EB_PAGE_SIZE) |
# lpt1 = # avol, # lpt0 = # avol, isbuf1 ↔ false, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, avol[pstate.lnum] = mapped(buf0), lpt1[pstate.lnum] = mklp(m1, # buf0, lpf, m4), adr = adr0, bleb = buffered(pstate.lnum), keyset(gch) = gc-heap(lpt1, log1), log = log1, lpt = lpt0, ns = ns0, pstate0 = pstate, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, pstate.lnum < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, buffered(pstate.lnum)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(true, buffered(pstate.lnum), lpt1, avol), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt1, avol), bufs-log-only(buffered(pstate.lnum), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), is-aligned(# buf0, 2 * NODE_HEADER_SIZE), log-group-block(log1, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log1), # buf0 ≤ LEB_SIZE, istore0 ⊑ istore, ⌊err⌋ , pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? ∨ pstate.journal? ⊦ ⟨apersistence_sync#(adr0, istore, istore0, ginval, gstore, gstore0, log1, m, ns0; pstate, isbuf1; err0)⟩ ( ginval < # lpt1 ∧ (isbuf1 → synced(avol)) ∧ pstate ≠ unbuffered ∧ (pstate = readonly ↔ true) ∧ (pstate ≠ readonly → pstate0.lnum = pstate.lnum) ∧ err = err0), buf1 = mkbuf(0), lpf = LP_FREE, pstate = unbuffered, pstate = readonly, dups(log1), is-aligned(# buf0, EB_PAGE_SIZE)