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Proof step 118 from proof inv-read-gblock-nodes (previous step)

# gndx3 = # lax1, # gndx0 = # lax2, # lpt0 = # avol, # lpt = # avol, LEB_SIZE = n0 + # buf0 + # buf, avol[m5] = mapped(buf0 + buf), # buf < 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), m5 < # avol, abs-nodes(buf, # buf0, gndx0, lax2, true), abs-nodes(buf0, gndx3, lax1, false), awbuf-inv(avol, bleb), buf-ro-rw-mode(isbuf, bleb, lpt0, avol), bufs-log-only(bleb, log0, lpt0), is-aligned(# buf, NODE_HEADER_SIZE), is-encoded(nodeheader(m, boolvar), subarray(buf, 0, NODE_HEADER_SIZE)), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), # buf0 + 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) ≤ LEB_SIZE, # buf0 + # buf ≤ LEB_SIZE, # buf0 + NODE_HEADER_SIZE ≤ LEB_SIZE ⊦ # buf + n0 = 0, gndx0 = [], isempty(buf, 0, NODE_HEADER_SIZE), range=(buf, NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE)

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 5 flags: discard

Additional information

Used simplifier rules: ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m + n; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)% ⊦ buf + mkbuf(0) = buf; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # mkbuf(n) = n; (s)% ⊦ n + 0 = n; (s)% ⊦ abs-nodes(mkbuf(0), m, gndx, lax, weak) ↔ gndx = [] ∧ lax = []; (s)%# buf ≠ 0 ⊦ abs-nodes(buf, m, gndx, lax, weak) → (NODE_HEADER_SIZE ≤ # buf + n ↔ NODE_HEADER_SIZE ≤ # buf); (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%m ≠ 0 ⊦ is-aligned(n, m) → (m ≤ n ↔ n ≠ 0); (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m ≤ n ↔ ¬ n < m; (ss)%m ≠ 0 ⊦ is-aligned(n, m) → (n < m ↔ n = 0); (s)%NODE_HEADER_SIZE ≤ # buf ⊦ is-encoded (nodeheader(m, boolvar0), subarray(buf, 0, NODE_HEADER_SIZE)) ∧ # buf < 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) → ( abs-nodes(buf, n, gndx, lax, weak) ↔ abs-failed(buf) ∧ gndx = [] ∧ lax = [] ∧ weak); (s)