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Proof step 48 from proof inv-read-gblock-nodes (previous step)

# gndx = # lax, # lpt = # avol, # lpt0 = # avol, avol[m5] = mapped(buf1), ax1 = ax0, buf = copy(avol[m5].data + mkempbuf(LEB_SIZE - # avol[m5].data), 0, buf0, 0, LEB_SIZE), buf0 = mkbuf(LEB_SIZE), err = err1, err = ESUCCESS, err2 = ESUCCESS, err2 = err0, gndx2 = gndx1, m0 = m, m1 = 0, m2 = LEB_SIZE, m3 = m5, avol[m5].mapped?, m5 < # avol, m0 < m2, abs-nodes(buf1, gndx, lax, true), awbuf-inv(avol, bleb), buf-ro-rw-mode(isbuf, bleb, lpt0, avol), bufs-log-only(bleb, log0, lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), 0 + LEB_SIZE ≤ # buf0, 0 + LEB_SIZE ≤ #(avol[m5].data + mkempbuf(LEB_SIZE - # avol[m5].data)), m0 + NODE_HEADER_SIZE ≤ # buf, LEB_SIZE ≥ # avol[m5].data, err = ESUCCESS ∨ err = ENOENT → read-gblock-inv(m3, m0, ax, gndx0, ax1, gndx2, avol[m3].data, err = ENOENT), ⌊err0⌋ ∨ err0 = ESUCCESS, err = ESUCCESS ∨ err = ENOENT ∨ ⌊err⌋ ⊦ ⟪decode_header#(m0, buf; ndhd; err); if err ≠ ESUCCESS then debug#("persistence: read_gblock_nodes could not decode header in LEB " + m3.toString + " at offset " + m0.toString) else let m = 2 * NODE_HEADER_SIZE + align↑(ndhd.size, 2 * NODE_HEADER_SIZE) in {if m2 < m0 + m then {debug# ("persistence: read_gblock_nodes ignoring node of size " + m.toString + " at offset " + m0.toString + " in LEB " + m3.toString); err := ENOENT} else if ¬ range=(buf, m0 + NODE_HEADER_SIZE + align↑(ndhd.size, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE) then {err := ENOENT; debug#("persistence: read_gblock_nodes partial node at offset " + m0.toString + " in LEB " + m3.toString)} else if ¬ ndhd.ispadding then let gnd = ? in {decode_group_node#(m0, m, buf; gnd; err); if err ≠ ESUCCESS then debug# ("persistence: read_gblock_nodes could not decode node at offset " + m0.toString + " in LEB " + m3.toString) else {gndx0 := gndx0 + gnd '; ax := ax + @(m3, m0, m) '}}; if err = ESUCCESS then m0 := m0 + m}⟫ ( ( (err = ESUCCESS ∨ err = ENOENT ∨ ⌊err⌋ ) ∧ (err = ESUCCESS ∨ err = ENOENT → read-gblock-inv(m3, m0, ax, gndx0, ax1, gndx2, avol[m3].data, err = ENOENT))) ∧ (err ≠ ESUCCESS ⊃ 0;m2 - m0) < (err1 ≠ ESUCCESS ⊃ 0;m2 - m)), isempty(buf, m0, NODE_HEADER_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 49:
# lpt0 = # avol, # lpt = # avol, # gndx = # lax, avol[m5] = mapped(buf1), m < # buf1 + (LEB_SIZE - # buf1), m < 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), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), read-gblock-inv(m5, m, ax, gndx0, ax1, gndx2, buf1, false), # buf1 ≤ LEB_SIZE, m + NODE_HEADER_SIZE ≤ # buf1 + (LEB_SIZE - # buf1), LEB_SIZE ≤ # buf1 + (LEB_SIZE - # buf1), ¬ isempty(buf1 + mkempbuf(LEB_SIZE - # buf1), m, NODE_HEADER_SIZE) ⊦ ⟪decode_header#(m, copy(avol[m5].data + mkempbuf(LEB_SIZE - # avol[m5].data), 0, mkbuf(LEB_SIZE), 0, LEB_SIZE); ndhd; err); m2 := LEB_SIZE; m0 := m; if err ≠ ESUCCESS then debug#("persistence: read_gblock_nodes could not decode header in LEB " + m5.toString + " at offset " + m0.toString) else let m = 2 * NODE_HEADER_SIZE + align↑(ndhd.size, 2 * NODE_HEADER_SIZE) in {if m2 < m0 + m then {debug# ("persistence: read_gblock_nodes ignoring node of size " + m.toString + " at offset " + m0.toString + " in LEB " + m5.toString); err := ENOENT} else if ¬ range= (copy(avol[m5].data + mkempbuf(LEB_SIZE - # avol[m5].data), 0, mkbuf(LEB_SIZE), 0, LEB_SIZE), m0 + NODE_HEADER_SIZE + align↑(ndhd.size, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE) then {err := ENOENT; debug#("persistence: read_gblock_nodes partial node at offset " + m0.toString + " in LEB " + m5.toString)} else if ¬ ndhd.ispadding then let gnd = ? in {decode_group_node# (m0, m, copy(avol[m5].data + mkempbuf(LEB_SIZE - # avol[m5].data), 0, mkbuf(LEB_SIZE), 0, LEB_SIZE); gnd; err); 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;m2 - m0) < m2 - m)

Rule argument

Additional information

Used simplifier rules: elim-mapped: ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf));% ⊦ m = m + n ↔ n = 0; (s)% ⊦ m ≤ m + n; (s)% ⊦ LEB_SIZE ≠ 0; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ ESUCCESS ≠ ENOENT; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ m ≤ m; (s)% ⊦ n + 0 = n; (s)%# buf = m, # buf0 = m ⊦ copy(buf, 0, buf0, 0, m) = buf; (s)% ⊦ # mkbuf(n) = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1; (s)%⊦ awbuf-inv(avol, bleb) ∧ n < # avol ∧ avol[n] = mapped(buf) → ¬ LEB_SIZE < # buf; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%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)% ⊦ n ≥ m ↔ m ≤ n; (s)