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Proof step 171 from proof inv-read-gblock-nodes (previous step)

# lpt0 = # avol, # lpt = # avol, # buf2 = gnd.alignedsize + 2 * NODE_HEADER_SIZE, # gndx3 = # lax1, # gndx1 = # lax0, LEB_SIZE = n0 + # buf0 + # buf2 + # buf1, avol[m5] = mapped(buf0 + buf2 + buf1), align↑(m2, 2 * NODE_HEADER_SIZE) = gnd.alignedsize, m5 < # avol, abs-node(buf2, gnd), abs-nodes(buf1, # buf0 + # buf2, gndx1, lax0, 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-aligned(# buf2, NODE_HEADER_SIZE), is-encoded(nodeheader(m2, false), 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 + gnd.alignedsize, validtrailer, 0, NODE_HEADER_SIZE), # buf0 + # buf2 ≤ LEB_SIZE, # buf0 + # buf2 + # buf1 ≤ LEB_SIZE, # buf0 + NODE_HEADER_SIZE ≤ LEB_SIZE ⊦ buf2 + buf1 = mkbuf(0), isempty(buf2, 0, NODE_HEADER_SIZE), ∃ gndx5, lax4, buf4, buf3. buf0 + buf2 + buf1 = buf4 + buf3 ∧ # buf4 = # buf0 + # buf2 ∧ abs-nodes(buf4, gndx3 + gnd ', lax1 + @(# buf0, # buf2) ', false) ∧ abs-nodes(buf3, # buf4, gndx5, lax4, true)

User applied rule exists right

And closed the goal!

Rule argument

pos: right 3 terms: gndx1, lax0, 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)% ⊦ 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 + gndx0 = gndx + gndx1 ↔ gndx0 = gndx1; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ lax + lax0 = lax + lax1 ↔ lax0 = lax1; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]%⊦ abs-nodes(buf, m, gndx, lax0, true) → (abs-nodes(buf, m, gndx0, lax1, true) ↔ gndx = gndx0 ∧ lax0 = lax1); (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%⊦ abs-node(buf, gnd) → ( abs-nodes(buf, m, gnd ', ladr ', false) ↔ ladr = @(m, gnd.flashsize)); (ss)% ⊦ gnd.flashsize = 2 * NODE_HEADER_SIZE + gnd.alignedsize; (s)% ⊦ @(m, m0) = @(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s) Used terms: gndx1, lax0, buf0 + buf2, buf1