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Proof step 112 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, 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 + 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 + mkempbuf(n0), NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 113:
⊦ is-aligned(# buf, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → (range=(buf + mkempbuf(n), m, validtrailer, 0, NODE_HEADER_SIZE) ↔ range=(buf, m, validtrailer, 0, NODE_HEADER_SIZE))
Proof step 114:
# lpt = # avol, # lpt0 = # avol, # gndx0 = # lax2, # gndx3 = # lax1, LEB_SIZE = n0 + # buf0 + # buf, avol[m5] = mapped(buf0 + buf), m5 < # avol, abs-nodes(buf0, gndx3, lax1, false), abs-nodes(buf, # buf0, gndx0, lax2, true), 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-aligned(NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), 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 + NODE_HEADER_SIZE ≤ LEB_SIZE, # buf0 + # buf ≤ LEB_SIZE, # buf0 + 2 * NODE_HEADER_SIZE + align↑(m, 2 * 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)

Rule argument

spec: <toplevel> name: range-eq-validtrailer seq: ⊦ is-aligned(# buf, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → ( range= (buf + mkempbuf(n), m, validtrailer, 0, NODE_HEADER_SIZE) ↔ range=(buf, m, validtrailer, 0, NODE_HEADER_SIZE)) subst: [m, n, buf] → [NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), n0, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ abs-nodes(buf, m, gndx, lax, weak) → is-aligned(# buf, NODE_HEADER_SIZE); (ss)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%m ≠ 0, n ≠ 0 ⊦ is-aligned(align↑(n0, n * m), m); (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%n ≠ 0 ⊦ is-aligned(n, n); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), n0, buf