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Proof step 199 from proof inv-read-gblock-nodes (previous step)

# gndx0 = # lax2, # gndx3 = # lax1, # lpt0 = # avol, # lpt = # avol, LEB_SIZE = n0 + # buf0 + (2 * NODE_HEADER_SIZE + m) + # buf1, avol[m5] = mapped(buf0 + buf2 + buf1), m5 < # avol, abs-nodes(buf0, gndx3, lax1, false), abs-nodes(buf1, # buf0 + 2 * NODE_HEADER_SIZE + m, gndx0, lax2, true), abs-padding(buf2), awbuf-inv(avol, bleb), buf-ro-rw-mode(isbuf, bleb, lpt0, avol), bufs-log-only(bleb, log0, lpt0), is-aligned(m, NODE_HEADER_SIZE), is-encoded(nodeheader(m, true), subarray(buf2, 0, NODE_HEADER_SIZE)), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), range=(buf2 + buf1, NODE_HEADER_SIZE + m, validtrailer, 0, NODE_HEADER_SIZE), # buf0 + 2 * NODE_HEADER_SIZE + m ≤ LEB_SIZE, # buf0 + (2 * NODE_HEADER_SIZE + m) + # buf1 ≤ LEB_SIZE, # buf0 + NODE_HEADER_SIZE ≤ LEB_SIZE ⊦ buf2 + buf1 = mkbuf(0), isempty(buf2, 0, NODE_HEADER_SIZE), ∃ gndx, lax, buf, buf3. buf0 + buf2 + buf1 = buf + buf3 ∧ # buf = # buf0 + 2 * NODE_HEADER_SIZE + m ∧ abs-nodes(buf, gndx3, lax1, false) ∧ abs-nodes(buf3, # buf, gndx, lax, true)

User applied rule exists right

And closed the goal!

Rule argument

pos: right 3 terms: gndx0, lax2, buf0 + buf2, buf1 abort: F discard: T computed: F

Additional information

Used simplifier rules: append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)%⊦ abs-padding(buf) ∧ is-encoded (nodeheader(m, true), subarray(buf, 0, NODE_HEADER_SIZE)) → # buf = 2 * NODE_HEADER_SIZE + m; (s)% ⊦ 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%⊦ abs-nodes(buf0, gndx, lax0, false) → ( abs-nodes(buf0 + buf1, gndx0, lax1, boolvar1) ↔ (∃ gndx1, lax2. gndx0 = gndx + gndx1 ∧ lax1 = lax0 + lax2 ∧ abs-nodes(buf1, # buf0, gndx1, lax2, boolvar1))); (s)% ⊦ gndx = gndx + gndx0 ↔ gndx0 = []; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ lax = lax + lax0 ↔ lax0 = []; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]%⊦ abs-padding(buf) → (abs-nodes(buf, m, gndx, lax, weak) ↔ gndx = [] ∧ lax = []); (s)%⊦ abs-nodes(buf, m, gndx, lax0, true) → (abs-nodes(buf, m, gndx0, lax1, true) ↔ gndx = gndx0 ∧ lax0 = lax1); (s) Used terms: gndx0, lax2, buf0 + buf2, buf1