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Proof step 181 from proof inv-read-gblock-nodes (previous step)

# lpt0 = # avol, # lpt = # avol, # gndx = # lax, LEB_SIZE = n0 + # buf1, avol[m5] = mapped(buf1), m1 < 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), is-encoded(nodeheader(m, true), subarray(buf1 + mkempbuf(n0), m1, NODE_HEADER_SIZE)), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), range=(buf1 + mkempbuf(n0), m1 + NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), read-gblock-inv(m5, m1, ax, gndx0, ax1, gndx2, buf1, false), m1 + 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) ≤ LEB_SIZE, # buf1 ≤ LEB_SIZE, m1 + NODE_HEADER_SIZE ≤ LEB_SIZE ⊦ isempty(buf1 + mkempbuf(n0), m1, NODE_HEADER_SIZE), ∃ gndx1, gndx3, lax0, lax1, buf, buf0. ax = ax1 + lax0.to-adr(m5) ∧ gndx0 = gndx2 + gndx1 ∧ buf1 = buf + buf0 ∧ # buf = m1 + 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) ∧ abs-nodes(buf, gndx1, lax0, false) ∧ abs-nodes(buf0, # buf, gndx3, lax1, true)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 182:
⊦ read-gblock-inv(m, n, ax, gndx, ax0, gndx0, buf, boolvar) ↔ (∃ gndx1, gndx2, lax1, lax2, buf0, buf1. ax = ax0 + lax1.to-adr(m) ∧ gndx = gndx0 + gndx1 ∧ buf = buf0 + buf1 ∧ # buf0 = n ∧ abs-nodes(buf0, gndx1, lax1, false) ∧ abs-nodes(buf1, # buf0, gndx2, lax2, true) ∧ (boolvar → gndx2 = [] ∧ lax2 = []))
Proof step 183:
# gndx = # lax, # lpt = # avol, # lpt0 = # avol, LEB_SIZE = n0 + # buf1, avol[m5] = mapped(buf1), m5 < # avol, m1 < LEB_SIZE, abs-nodes(buf1, gndx, lax, true), awbuf-inv(avol, bleb), buf-ro-rw-mode(isbuf, bleb, lpt0, avol), bufs-log-only(bleb, log0, lpt0), is-encoded(nodeheader(m, true), subarray(buf1 + mkempbuf(n0), m1, NODE_HEADER_SIZE)), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), range=(buf1 + mkempbuf(n0), m1 + NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), m1 + NODE_HEADER_SIZE ≤ LEB_SIZE, # buf1 ≤ LEB_SIZE, m1 + 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) ≤ LEB_SIZE, ∃ gndx1, gndx3, lax1, lax2, buf0, buf2. ax = ax1 + lax1.to-adr(m5) ∧ gndx0 = gndx2 + gndx1 ∧ buf1 = buf0 + buf2 ∧ # buf0 = m1 ∧ abs-nodes(buf0, gndx1, lax1, false) ∧ abs-nodes(buf2, # buf0, gndx3, lax2, true) ∧ (false → gndx3 = [] ∧ lax2 = []) ⊦ isempty(buf1 + mkempbuf(n0), m1, NODE_HEADER_SIZE), ∃ gndx1, gndx3, lax0, lax1, buf, buf0. ax = ax1 + lax0.to-adr(m5) ∧ gndx0 = gndx2 + gndx1 ∧ buf1 = buf + buf0 ∧ # buf = m1 + 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) ∧ abs-nodes(buf, gndx1, lax0, false) ∧ abs-nodes(buf0, # buf, gndx3, lax1, true)

Rule argument

spec: persistence-base name: read-gblock-inv seq: ⊦ read-gblock-inv(m, n, ax, gndx, ax0, gndx0, buf, boolvar) ↔ (∃ gndx1, gndx2, lax1, lax2, buf0, buf1. ax = ax0 + lax1.to-adr(m) ∧ gndx = gndx0 + gndx1 ∧ buf = buf0 + buf1 ∧ # buf0 = n ∧ abs-nodes(buf0, gndx1, lax1, false) ∧ abs-nodes(buf1, # buf0, gndx2, lax2, true) ∧ (boolvar → gndx2 = [] ∧ lax2 = [])) subst: [boolvar, buf, gndx0, ax0, gndx, ax, n, m] → [false, buf1, gndx2, ax1, gndx0, ax, m1, m5] flags: <all paths>

Additional information

Used terms: false, buf1, gndx2, ax1, gndx0, ax, m1, m5