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Proof step 147 from proof refine-sync (previous step)

# lpt0 = # avol0, # lpt1 = # avol0, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, gstore2[pstate.lnum] = groupblock(gndx, lax, m), avol0[pstate.lnum] = mapped(buf0), lpt1[pstate.lnum] = mklp(m, # buf0, LP_GROUP_NODES, m7), 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-istore(avol0, lpt1, istore2), abs-leb(mapped(buf0), groupblock(gndx, lax, m), mklp(m, # buf0, LP_GROUP_NODES, m7)), 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(groupblock(gndx, lax, m)), inv(gstore2 \ ginval), inv(gstore1), inv(istore2), inv(istore1), 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(m, # buf0 + # buf1, LP_GROUP_NODES, m7)], lpt0, log1), lpt-ram-flash(lpt1, lpt0, log1), pstate.lnum ∈ gstore2, 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.index? → pstate.lnum ∈ istore2, pstate.index? ∨ pstate.journal? ⊦ buf1 = mkbuf(0), pstate = readonly, pstate = unbuffered, dups(log1), is-aligned(# buf0, EB_PAGE_SIZE), pstate.lnum ∈ ginval, mapped(buf0 + buf1).mapped? ∧ abs-nodes (mapped(buf0 + buf1).data, groupblock(gndx, lax, m).gndlist, groupblock(gndx, lax, m).ladrlist, mklp(m, # buf0 + # buf1, LP_GROUP_NODES, m7).size = LEB_SIZE) ∧ ( mklp(m, # buf0 + # buf1, LP_GROUP_NODES, m7).size ≠ LEB_SIZE → mklp(m, # buf0 + # buf1, LP_GROUP_NODES, m7).size = # mapped(buf0 + buf1).data)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 148:
# lpt1 = # avol0, # lpt0 = # avol0, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, lpt1[pstate.lnum] = mklp(m, # buf0, LP_GROUP_NODES, m7), avol0[pstate.lnum] = mapped(buf0), gstore2[pstate.lnum] = groupblock(gndx, lax, m), 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-istore(avol0, lpt1, istore2), abs-leb(mapped(buf0), groupblock(gndx, lax, m), mklp(m, # buf0, LP_GROUP_NODES, m7)), 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(istore1), inv(istore2), inv(gstore1), inv(gstore2 \ ginval), inv(groupblock(gndx, lax, m)), 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(m, # buf0 + # buf1, LP_GROUP_NODES, m7)], lpt0, log1), pstate.lnum ∈ gstore2, # buf0 + # buf1 ≤ LEB_SIZE, # buf0 ≤ LEB_SIZE, EB_PAGE_SIZE + # buf0 ≤ LEB_SIZE + # buf0 % EB_PAGE_SIZE, istore1 ⊑ istore2, pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last, pstate.index? ∨ pstate.journal? ⊦ buf1 = mkbuf(0), pstate = unbuffered, pstate = readonly, abs-nodes(buf0 + buf1, gndx, lax, # buf0 + # buf1 = LEB_SIZE), dups(log1), is-aligned(# buf0, EB_PAGE_SIZE), pstate.lnum ∈ ginval

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ mklp(n2, n3, lpf, m).size = n3; (s)% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)% ⊦ groupblock(gndx, lax, m).gndlist = gndx; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf).mapped?; (s)