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Proof step 274 from proof refine-sync (previous step)

# indx = # lax, # lpt0 = # avol0, # lpt1 = # avol0, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, istore2[pstate.lnum] = indexblock(indx, lax, m1), lpt1[pstate.lnum] = mklp(m1, # buf, LP_INDEX_NODES, m3), avol0[pstate.lnum] = mapped(buf), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, n < # buf1, ginval < # avol0, pstate.lnum < # avol0, abs-gstore(avol0, lpt1, gstore2, ginval), abs-nodes(buf, indx, lax, # buf = LEB_SIZE), abs-padding(buf1), awbuf-inv(avol0[pstate.lnum, mapped(buf + subarray(buf1, 0, n))], 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(indexblock(indx, lax, m1)), inv(gstore2 \ ginval), inv(gstore1), inv(istore2), inv(istore1), is-aligned(# buf, 2 * NODE_HEADER_SIZE), 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[pstate.lnum, mklp(m1, LEB_SIZE, LP_INDEX_NODES, m3)], lpt0, log1), pstate.lnum ∈ istore2, # buf ≤ LEB_SIZE, # buf + # buf1 ≤ LEB_SIZE, istore1 ⊑ istore2, ⌊err1⌋ , pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? ∨ pstate.journal? ⊦ # buf = LEB_SIZE, buf1 = mkbuf(0), n = 0, pstate = unbuffered, pstate = readonly, abs-nodes(buf + subarray(buf1, 0, n), indx, lax, true), dups(log1), is-aligned(# buf, EB_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 275:
# indx = # lax, # lpt0 = # avol0, # lpt1 = # avol0, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, istore2[pstate.lnum] = indexblock(indx, lax, m1), lpt1[pstate.lnum] = mklp(m1, # buf, LP_INDEX_NODES, m3), avol0[pstate.lnum] = mapped(buf), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, # buf < LEB_SIZE, n < # buf1, ginval < # avol0, pstate.lnum < # avol0, abs-gstore(avol0, lpt1, gstore2, ginval), abs-nodes(buf, indx, lax, false), abs-padding(buf1), awbuf-inv(avol0[pstate.lnum, mapped(buf + subarray(buf1, 0, n))], 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(indexblock(indx, lax, m1)), inv(gstore2 \ ginval), inv(gstore1), inv(istore2), inv(istore1), is-aligned(# buf, 2 * NODE_HEADER_SIZE), 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[pstate.lnum, mklp(m1, LEB_SIZE, LP_INDEX_NODES, m3)], lpt0, log1), pstate.lnum ∈ istore2, # buf + # buf1 ≤ LEB_SIZE, istore1 ⊑ istore2, ⌊err1⌋ , pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? ∨ pstate.journal? ⊦ # buf = LEB_SIZE, buf1 = mkbuf(0), n = 0, pstate = unbuffered, pstate = readonly, abs-nodes(subarray(buf1, 0, n), # buf, [], [], true), dups(log1), is-aligned(# buf, EB_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: ⊦ LEB_SIZE ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%⊦ abs-nodes(buf0, indx, lax0, false) → ( abs-nodes(buf0 + buf1, indx, lax0, weak) ↔ abs-nodes(buf1, # buf0, [], [], weak)); (ss)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)