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Proof step 87 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), m5 < # avol, # buf < 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), LEB_SIZE < # buf0 + 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), n0 + # buf < 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), 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-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 + # buf ≤ LEB_SIZE, # buf0 + NODE_HEADER_SIZE ≤ LEB_SIZE ⊦ # buf + n0 = 0, gndx0 = [], isempty(buf + mkempbuf(n0), 0, NODE_HEADER_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 88:
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)

Rule argument

spec: abs-list, inst: encoding-group-node name: abs-nodes-nospace-header-h seq: 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) subst: [m, boolvar0, weak, lax, gndx, n, buf] → [m, boolvar, true, lax2, gndx0, # buf0, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ is-encoded(ndhd, buf) → (is-encoded(ndhd0, buf) ↔ ndhd = ndhd0); (s)% ⊦ 2 * m = 0 ↔ m = 0; (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%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)%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%# buf < NODE_HEADER_SIZE ⊦ abs-nodes(buf, m, gndx, lax, boolvar) ↔ gndx = [] ∧ lax = [] ∧ buf = mkbuf(0); (ws)% ⊦ ¬ m < n → ¬ m + m0 < n; (s) Used terms: m, boolvar, true, lax2, gndx0, # buf0, buf