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Proof step 196 from proof refine-add-ind (previous step)

# lpt0 = # avol, # buf1 = 2 * NODE_HEADER_SIZE + ind.alignedsize, # lpt1 = # avol, # indx0 = # lax0, avol[m1] = mapped(buf), istore[m1] = indexblock(indx0, lax0, m0), lpt1[m1] = mklp(m0, # buf, LP_INDEX_NODES, m4), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, m1 < # avol, n < # buf1, ginval < # avol, abs-gstore(avol, lpt1, gstore2, ginval), abs-node(buf1, ind), abs-nodes(buf, indx0, lax0, # buf = LEB_SIZE), awbuf-inv(avol[m1, mapped(buf + subarray(buf1, 0, n))], buffered(m1)), awbuf-inv(avol, buffered(m1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(m1), lpt1, avol), bufs-log-only(buffered(m1), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore1), freelist-cons(lpt1, freelist), inv(gstore2 \ ginval), inv(gstore1), inv(istore), inv(istore0), inv(indexblock(indx0, lax0, m0)), is-aligned(# buf + n, EB_PAGE_SIZE), log-group-block(log1, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log1), lpt-ram-flash(lpt1[m1, mklp(m0, LEB_SIZE, LP_INDEX_NODES, m4)], lpt0, log1), m1 ∈ istore, # buf + # buf1 ≤ LEB_SIZE, istore0 ⊑ istore, ⌊err1⌋ , isbuf → synced(avol) ⊦ buf1 = mkbuf(0), n = 0, abs-nodes(buf + subarray(buf1, 0, n), indx0, lax0, true), dups(log1)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 197:
# indx0 = # lax0, # lpt1 = # avol, # buf1 = 2 * NODE_HEADER_SIZE + ind.alignedsize, # lpt0 = # avol, lpt1[m1] = mklp(m0, # buf, LP_INDEX_NODES, m4), istore[m1] = indexblock(indx0, lax0, m0), avol[m1] = mapped(buf), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore1) = gstore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, ginval < # avol, n < # buf1, m1 < # avol, abs-gstore(avol, lpt1, gstore2, ginval), abs-node(buf1, ind), abs-nodes(buf, indx0, lax0, # buf = LEB_SIZE), awbuf-inv(avol, buffered(m1)), awbuf-inv(avol[m1, mapped(buf + subarray(buf1, 0, n))], buffered(m1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(m1), lpt1, avol), bufs-log-only(buffered(m1), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore1), freelist-cons(lpt1, freelist), inv(indexblock(indx0, lax0, m0)), inv(istore0), inv(istore), inv(gstore1), inv(gstore2 \ ginval), is-aligned(# buf + n, EB_PAGE_SIZE), log-group-block(log1, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1[m1, mklp(m0, LEB_SIZE, LP_INDEX_NODES, m4)], lpt0, log1), lpt-ram-flash(lpt1, lpt0, log1), m1 ∈ istore, # buf + # buf1 ≤ LEB_SIZE, istore0 ⊑ istore, ⌊err1⌋ , isbuf → synced(avol) ⊦ # buf = LEB_SIZE, buf1 = mkbuf(0), n = 0, abs-nodes(buf + subarray(buf1, 0, n), indx0, lax0, true), dups(log1)

Rule argument

fma: # buf = LEB_SIZE

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ is-aligned(LEB_SIZE, EB_PAGE_SIZE); (ss)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ lpt[n] = lp → lpt[n, lp] = lpt; (s)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s) Used formulas: # buf = LEB_SIZE