| # lpt0 = # avol[m, mapped(avol[m].data + subarray(buf1, 0, # buf1))], # buf1 = 2 * NODE_HEADER_SIZE + ind.alignedsize, # lpt1 = # avol, # lpt0 = # avol, isbuf ↔ false, avol[n] = mapped(buf0), lpt1[n] = mklp(m1, # buf0, LP_INDEX_NODES, m2), err = err0, err = ESUCCESS, keyset(gch) = gc-heap(lpt1, log0), m = buffered(n).leb, buffered(n).isbuf?, avol[m].mapped?, buffered(n).leb < # lpt1, m < # avol, n < # avol, abs-node(buf1, ind), awbuf-inv(avol[m, mapped(avol[m].data + subarray(buf1, 0, # buf1))], buffered(n)), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), log0, lpt1), freelist-cons(lpt1, freelist), log-group-block(log0, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log0), 0 + # buf1 ≤ # buf1, # buf0 + # buf1 ≤ LEB_SIZE, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪lpt1[buffered(n).leb] := mklp(lpt1[buffered(n).leb].ref-size, lpt1[buffered(n).leb].size + # buf1, lpt1[buffered(n).leb].flags, lpt1[buffered(n).leb].gcheapidx)⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(buffered(n), log0, lpt1) ∧ # lpt1 = # avol[m, mapped(avol[m].data + subarray(buf1, 0, # buf1))] ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf, buffered(n), lpt1, avol[m, mapped(avol[m].data + subarray(buf1, 0, # buf1))]) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0)) |
Used simplifier rules: elim-mapped: ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf));%elim-mapped: ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf));% ⊦ buffered(m).leb = m; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ # avol[n, aleb] = # avol; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m; (s)% ⊦ buffered(m).isbuf?; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)%⊦ lpt-free-unref(lpt) → ( lpt-free-unref(lpt[n, lp]) ↔ n < # lpt ∧ lp.flags = LP_FREE → lp.ref-size = 0); (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)% ⊦ LP_GROUP_NODES ≠ LP_INDEX_NODES; (s)%lpf0 ≠ LP_GROUP_NODES, n < # lpt ⊦ lpt[n] = mklp(m0, m1, lpf0, m2) ∧ keyset(gch) = gc-heap(lpt, nx) → ( bin-heap-inv(gch, lpt[n, mklp(n0, n1, lpf1, n2)]) ↔ bin-heap-inv(gch, lpt)); (s)%lpf0 ≠ LP_GROUP_NODES, lpf1 ≠ LP_GROUP_NODES, n < # lpt ⊦ lpt[n] = mklp(m0, m1, lpf0, m2) → gc-heap(lpt[n, mklp(n0, n1, lpf1, n2)], nx) = gc-heap(lpt, nx); (s)% ⊦ mklp(n2, n3, lpf, m).size = n3; (s)% ⊦ mklp(n2, n3, lpf, m).gcheapidx = m; (s)%lpt[n].flags = lp.flags ⊦ bufs-log-only(bleb, nx, lpt) → bufs-log-only(bleb, nx, lpt[n, lp]); (s)% ⊦ # lpt[n, lp] = # lpt; (s)%n < # lpt, lpf ≠ LP_GROUP_NODES ⊦ lpt[n] = mklp(n0, n1, lpf, n2) ∧ log-group-block(nx, lpt) → log-group-block(nx, lpt[n, lp]); (s)%n < # lpt, n < # avol ⊦ buf-ro-rw-mode (false, buffered(n), lpt[n, mklp(m0, m1, lpf, m2)], avol[n, mapped(buf)]) ↔ m1 = # buf; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ m + n = m + n0 ↔ n = n0; (s)%⊦ lpt-leb-size(lpt) → (lpt-leb-size(lpt[n, lp]) ↔ # lpt ≤ n ∨ lp.size ≤ LEB_SIZE); (s)% ⊦ m < n → (n ≤ m ↔ false); (s)%n < # lpt, lpf ≠ LP_GROUP_NODES ⊦ lpt-ram-flash(lpt, lpt0, nx) → lpt-ram-flash(lpt[n, mklp(n0, n1, lpf, n2)], lpt0, nx); (ss)%inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ LP_FREE ≠ LP_INDEX_NODES; (s)%⊦ freelist-cons(lpt, freelist) ∧ lpt[n] = mklp(m0, m1, lpf, m2) → freelist-cons(lpt[n, mklp(n0, n1, lpf, n2)], freelist); (s)