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Proof step 196 from proof inv-read-gblock-nodes (previous step)

# gndx3 = # lax1, # 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-failed(buf), 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, true), subarray(buf, 0, NODE_HEADER_SIZE)), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), range=(buf, NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), # 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, buf = mkbuf(0), isempty(buf, 0, NODE_HEADER_SIZE), ∃ gndx5, lax4, buf1, buf2. buf0 + buf = buf1 + buf2 ∧ # buf1 = # buf0 + 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) ∧ abs-nodes(buf1, gndx3, lax1, false) ∧ abs-nodes(buf2, # buf1, gndx5, lax4, true)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 197:
⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ (∀ n. n < m → buf[n0 + n] = buf0[n1 + n])

Rule argument

spec: array-splice, inst: buffer name: range-eq-ext seq: ⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ (∀ n. n < m → buf[n0 + n] = buf0[n1 + n]) subst: [m, n1, buf0, n0, buf] → [NODE_HEADER_SIZE, 0, validtrailer, NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)% ⊦ m ≤ m; (s)% ⊦ m + m = 2 * m; (s)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: NODE_HEADER_SIZE, 0, validtrailer, NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), buf