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Proof step 172 from proof refine-sync (previous step)

# lpt0 = # avol0, # lpt1 = # avol0, # indx = # lax, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, lpt1[pstate.lnum] = mklp(m0, # buf0, LP_INDEX_NODES, m3), istore2[pstate.lnum] = indexblock(indx, lax, m0), avol0[pstate.lnum] = mapped(buf0), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, ginval < # avol0, pstate.lnum < # avol0, abs-gstore(avol0, lpt1, gstore2, ginval), abs-nodes(buf0, indx, lax, # buf0 = LEB_SIZE), abs-padding(buf1), awbuf-inv(avol0[pstate.lnum, mapped(buf0 + buf1)], buffered(pstate.lnum)), awbuf-inv(avol0, buffered(pstate.lnum)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt1, avol0), bufs-log-only(buffered(pstate.lnum), log1, lpt1), flash-lpt-cons(lpt0, istore1, gstore1), freelist-cons(lpt1, freelist), inv(gstore2 \ ginval), inv(gstore1), inv(istore2), inv(istore1), inv(indexblock(indx, lax, m0)), is-aligned(# buf0, 2 * NODE_HEADER_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[pstate.lnum, mklp(m0, # buf0 + # buf1, LP_INDEX_NODES, m3)], lpt0, log1), lpt-ram-flash(lpt1, lpt0, log1), pstate.lnum ∈ istore2, EB_PAGE_SIZE + # buf0 ≤ LEB_SIZE + # buf0 % EB_PAGE_SIZE, # buf0 ≤ LEB_SIZE, # buf0 + # buf1 ≤ LEB_SIZE, istore1 ⊑ istore2, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? ∨ pstate.journal? ⊦ buf1 = mkbuf(0), pstate = readonly, pstate = unbuffered, abs-leb(mapped(buf0 + buf1), indexblock(indx, lax, m0), mklp(m0, # buf0 + # buf1, LP_INDEX_NODES, m3)), dups(log1), is-aligned(# buf0, EB_PAGE_SIZE)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 173:
# indx = # lax, # lpt1 = # avol0, # lpt0 = # avol0, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, avol0[pstate.lnum] = mapped(buf0), istore2[pstate.lnum] = indexblock(indx, lax, m0), lpt1[pstate.lnum] = mklp(m0, # buf0, LP_INDEX_NODES, m3), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, pstate.lnum < # avol0, ginval < # avol0, abs-gstore(avol0, lpt1, gstore2, ginval), abs-nodes(buf0, indx, lax, # buf0 = LEB_SIZE), abs-padding(buf1), awbuf-inv(avol0, buffered(pstate.lnum)), awbuf-inv(avol0[pstate.lnum, mapped(buf0 + buf1)], buffered(pstate.lnum)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt1, avol0), bufs-log-only(buffered(pstate.lnum), log1, lpt1), flash-lpt-cons(lpt0, istore1, gstore1), freelist-cons(lpt1, freelist), inv(indexblock(indx, lax, m0)), inv(istore1), inv(istore2), inv(gstore1), inv(gstore2 \ ginval), is-aligned(# buf0, 2 * NODE_HEADER_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, lpt0, log1), lpt-ram-flash(lpt1[pstate.lnum, mklp(m0, # buf0 + # buf1, LP_INDEX_NODES, m3)], lpt0, log1), pstate.lnum ∈ istore2, # buf0 + # buf1 ≤ LEB_SIZE, # buf0 ≤ LEB_SIZE, EB_PAGE_SIZE + # buf0 ≤ LEB_SIZE + # buf0 % EB_PAGE_SIZE, istore1 ⊑ istore2, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? ∨ pstate.journal? ⊦ # buf0 = LEB_SIZE, buf1 = mkbuf(0), pstate = unbuffered, pstate = readonly, abs-leb(mapped(buf0 + buf1), indexblock(indx, lax, m0), mklp(m0, # buf0 + # buf1, LP_INDEX_NODES, m3)), dups(log1), is-aligned(# buf0, EB_PAGE_SIZE)

Rule argument

fma: # buf0 = LEB_SIZE

Additional information

Used simplifier rules: let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used formulas: # buf0 = LEB_SIZE