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Proof step 278 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, # 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-failed(subarray(buf1, 0, n)), dups(log1), is-aligned(# buf, EB_PAGE_SIZE), ∃ buf0, buf2. subarray(buf1, 0, n) = buf0 + buf2 ∧ abs-padding(buf0) ∧ abs-nodes(buf2, # buf + # buf0, [], [], true)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: abs-node, inst: encoding-group-node name: abs-padding-subarray-failed seq: n < # buf, n ≠ 0 ⊦ abs-padding(buf) ∧ is-aligned(n, NODE_HEADER_SIZE) → abs-failed(subarray(buf, 0, n)) subst: [n, buf] → [n, buf1] flags: <all paths>

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%⊦ abs-nodes(buf, indx, lax, boolvar) ∧ is-aligned(# buf + n, EB_PAGE_SIZE) → is-aligned(n, NODE_HEADER_SIZE); (s) Used terms: n, buf1