| # lpt0 = # avol, # buf1 = 2 * NODE_HEADER_SIZE + ind.alignedsize, # lpt1 = # avol, isbuf ↔ false, lpt1[m1] = mklp(m4, # buf, LP_INDEX_NODES, m2), istore[m1] = indexblock(indx, lax, m4), avol[m1] = mapped(buf), buf0 = buf1, err = err0, keyset(gch) = gc-heap(lpt1, log1), m = buffered(m1).leb, n0 = # buf1, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, buffered(m1).isbuf?, n < n0, ginval < # avol, m1 < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), abs-node(buf1, ind), awbuf-inv(avol, buffered(m1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(m1), lpt1, avol), bufs-log-only(buffered(m1), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(indexblock(indx, lax, m4)), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), is-aligned(# avol[m].data + n, EB_PAGE_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), m1 ∈ istore, # buf + # buf1 ≤ LEB_SIZE, istore0 ⊑ istore, n ≠ 0 → n < n0 → avol[m].mapped? ∧ m < # avol, isbuf1 → synced(avol), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ [avol[m] := mapped(avol[m].data + subarray(buf0, 0, n)); isbuf := true] ( awbuf-inv(avol, buffered(m1)) ∧ # lpt0 = # avol → [adr := adr2; if err = ESUCCESS then {adr := @(buffered(m1).leb, lpt1[buffered(m1).leb].size, # buf1); lpt1[buffered(m1).leb] := mklp (lpt1[buffered(m1).leb].ref-size, lpt1[buffered(m1).leb].size + # buf1, lpt1[buffered(m1).leb].flags, lpt1[buffered(m1).leb].gcheapidx)} else lpt1[buffered(m1).leb] := mklp(lpt1[buffered(m1).leb].ref-size, LEB_SIZE, lpt1[buffered(m1).leb].flags, lpt1[buffered(m1).leb].gcheapidx)] ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log1) ∧ bufs-log-only(buffered(m1), log1, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log1, lpt1) ∧ buf-ro-rw-mode(isbuf, buffered(m1), lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log1) → ⟨pstate := index(m1); apersistence_add_ind#(ind, adr0, istore0, ginval, gstore, gstore0, log1, m0, ns0; adr2, istore, pstate, isbuf1; err1)⟩ ( abs-istore(avol, lpt1, istore) ∧ abs-gstore(avol, lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (isbuf1 → synced(avol)) ∧ pstate ≠ unbuffered ∧ (pstate = readonly ↔ isbuf) ∧ (pstate ≠ readonly → m1 = pstate.lnum) ∧ adr = adr2 ∧ err = err1))), err = ESUCCESS, n = 0, dups(log1) |
# lpt1 = # avol, # buf1 = 2 * NODE_HEADER_SIZE + ind.alignedsize, # lpt0 = # avol, isbuf ↔ false, avol[m1] = mapped(buf), istore[m1] = indexblock(indx, lax, m4), lpt1[m1] = mklp(m4, # buf, LP_INDEX_NODES, m2), buf0 = buf1, err = err0, keyset(gch) = gc-heap(lpt1, log1), m = buffered(m1).leb, n0 = # buf1, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, buffered(m1).isbuf?, avol[m].mapped?, m < # avol, m1 < # avol, ginval < # avol, n < n0, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), abs-node(buf1, ind), awbuf-inv(avol, buffered(m1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(m1), lpt1, avol), bufs-log-only(buffered(m1), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), inv(indexblock(indx, lax, m4)), is-aligned(# avol[m].data + n, EB_PAGE_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), m1 ∈ istore, 0 + n ≤ # buf0, # buf + # buf1 ≤ LEB_SIZE, istore0 ⊑ istore, isbuf1 → synced(avol), n ≠ 0 → n < n0 → avol[m].mapped? ∧ m < # avol, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ [isbuf := true] ( awbuf-inv(avol[m, mapped(avol[m].data + subarray(buf0, 0, n))], buffered(m1)) ∧ # lpt0 = # avol[m, mapped(avol[m].data + subarray(buf0, 0, n))] → [adr := adr2; if err = ESUCCESS then {adr := @(buffered(m1).leb, lpt1[buffered(m1).leb].size, # buf1); lpt1[buffered(m1).leb] := mklp (lpt1[buffered(m1).leb].ref-size, lpt1[buffered(m1).leb].size + # buf1, lpt1[buffered(m1).leb].flags, lpt1[buffered(m1).leb].gcheapidx)} else lpt1[buffered(m1).leb] := mklp(lpt1[buffered(m1).leb].ref-size, LEB_SIZE, lpt1[buffered(m1).leb].flags, lpt1[buffered(m1).leb].gcheapidx)] ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log1) ∧ bufs-log-only(buffered(m1), log1, lpt1) ∧ # lpt1 = # avol[m, mapped(avol[m].data + subarray(buf0, 0, n))] ∧ log-group-block(log1, lpt1) ∧ buf-ro-rw-mode(isbuf, buffered(m1), lpt1, avol[m, mapped(avol[m].data + subarray(buf0, 0, n))]) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log1) → ⟨pstate := index(m1); apersistence_add_ind#(ind, adr0, istore0, ginval, gstore, gstore0, log1, m0, ns0; adr2, istore, pstate, isbuf1; err1)⟩ ( abs-istore(avol[m, mapped(avol[m].data + subarray(buf0, 0, n))], lpt1, istore) ∧ abs-gstore(avol[m, mapped(avol[m].data + subarray(buf0, 0, n))], lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (isbuf1 → synced(avol[m, mapped(avol[m].data + subarray(buf0, 0, n))])) ∧ pstate ≠ unbuffered ∧ (pstate = readonly ↔ isbuf) ∧ (pstate ≠ readonly → m1 = pstate.lnum) ∧ adr = adr2 ∧ err = err1))), err = ESUCCESS, n = 0, dups(log1)