[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 126 from proof inv-read-gblock-nodes (previous step)

# gndx = # lax, # lpt = # avol, # lpt0 = # avol, LEB_SIZE = n0 + # buf1, avol[m5] = mapped(buf1), buf0 = copy(avol[m5].data + mkempbuf(n0), 0, mkbuf(LEB_SIZE), 0, LEB_SIZE), m3 = 2 * NODE_HEADER_SIZE + align↑(m2, 2 * NODE_HEADER_SIZE), n1 = m1, m5 < # avol, m1 < LEB_SIZE, abs-nodes(buf1, gndx, lax, true), awbuf-inv(avol, bleb), buf-ro-rw-mode(isbuf, bleb, lpt0, avol), bufs-log-only(bleb, log0, lpt0), is-encoded(nodeheader(m2, false), subarray(buf1 + mkempbuf(n0), m1, NODE_HEADER_SIZE)), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), range=(buf1 + mkempbuf(n0), m1 + NODE_HEADER_SIZE + align↑(m2, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), read-gblock-inv(m5, m1, ax, gndx0, ax1, gndx2, buf1, false), m1 + NODE_HEADER_SIZE ≤ LEB_SIZE, # buf1 ≤ LEB_SIZE, m1 + 2 * NODE_HEADER_SIZE + align↑(m2, 2 * NODE_HEADER_SIZE) ≤ LEB_SIZE ⊦ [decode_group_node# (m1, 2 * NODE_HEADER_SIZE + align↑(m2, 2 * NODE_HEADER_SIZE), copy(avol[m5].data + mkempbuf(n0), 0, mkbuf(LEB_SIZE), 0, LEB_SIZE); gnd; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → abs-node(subarray(buf0, n1, m3), gnd) ∧ m3 = gnd.flashsize ∧ n1 + m3 ≤ # buf0) → ⟪m0 := m1; m := 2 * NODE_HEADER_SIZE + align↑(m2, 2 * NODE_HEADER_SIZE); if err ≠ ESUCCESS then debug#("persistence: read_gblock_nodes could not decode node at offset " + m0.toString + " in LEB " + m5.toString) else {gndx0 := gndx0 + gnd '; ax := ax + @(m5, m0, m) '}; if err = ESUCCESS then m0 := m0 + m⟫ ( (err = ESUCCESS ∨ err = ENOENT ∨ ⌊err⌋ ) ∧ (err = ESUCCESS ∨ err = ENOENT → read-gblock-inv(m5, m0, ax, gndx0, ax1, gndx2, avol[m5].data, err = ENOENT)) ∧ (err ≠ ESUCCESS ⊃ 0;LEB_SIZE - m0) + m1 < LEB_SIZE)), isempty(buf1 + mkempbuf(n0), m1, NODE_HEADER_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 127:
# lpt0 = # avol, # lpt = # avol, # gndx = # lax, LEB_SIZE = n0 + # buf1, avol[m5] = mapped(buf1), m1 < LEB_SIZE, m5 < # avol, abs-nodes(buf1, gndx, lax, true), awbuf-inv(avol, bleb), buf-ro-rw-mode(isbuf, bleb, lpt0, avol), bufs-log-only(bleb, log0, lpt0), is-encoded(nodeheader(m2, false), subarray(buf1 + mkempbuf(n0), m1, NODE_HEADER_SIZE)), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), range=(buf1 + mkempbuf(n0), m1 + NODE_HEADER_SIZE + align↑(m2, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), read-gblock-inv(m5, m1, ax, gndx0, ax1, gndx2, buf1, false), m1 + 2 * NODE_HEADER_SIZE + align↑(m2, 2 * NODE_HEADER_SIZE) ≤ LEB_SIZE, # buf1 ≤ LEB_SIZE, m1 + NODE_HEADER_SIZE ≤ LEB_SIZE, ¬ isempty(buf1 + mkempbuf(n0), m1, NODE_HEADER_SIZE) ⊦ [decode_group_node# (m1, 2 * NODE_HEADER_SIZE + align↑(m2, 2 * NODE_HEADER_SIZE), copy(avol[m5].data + mkempbuf(n0), 0, mkbuf(LEB_SIZE), 0, LEB_SIZE); gnd; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → abs-node(subarray(avol[m5].data + mkempbuf(n0), m1, 2 * NODE_HEADER_SIZE + align↑(m2, 2 * NODE_HEADER_SIZE)), gnd) ∧ align↑(m2, 2 * NODE_HEADER_SIZE) = gnd.alignedsize ∧ m1 + 2 * NODE_HEADER_SIZE + align↑(m2, 2 * NODE_HEADER_SIZE) ≤ # avol[m5].data + n0) → ⟪m0 := m1; m := 2 * NODE_HEADER_SIZE + align↑(m2, 2 * NODE_HEADER_SIZE); if err ≠ ESUCCESS then debug#("persistence: read_gblock_nodes could not decode node at offset " + m0.toString + " in LEB " + m5.toString) else {gndx0 := gndx0 + gnd '; ax := ax + @(m5, m0, m) '}; if err = ESUCCESS then m0 := m0 + m⟫ ( (err = ESUCCESS ∨ err = ENOENT ∨ ⌊err⌋ ) ∧ (err = ESUCCESS ∨ err = ENOENT → read-gblock-inv(m5, m0, ax, gndx0, ax1, gndx2, avol[m5].data, err = ENOENT)) ∧ (err ≠ ESUCCESS ⊃ 0;LEB_SIZE - m0) + m1 < LEB_SIZE))

Rule argument

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ gnd.flashsize = 2 * NODE_HEADER_SIZE + gnd.alignedsize; (s)%# buf = m, # buf0 = m ⊦ copy(buf, 0, buf0, 0, m) = buf; (s)% ⊦ # mkbuf(n) = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # mkempbuf(n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ mapped(buf).data = buf; (s)