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Proof step 225 from proof refine-add-gnds (previous step)

# gndx1 = # lax1, # gndx0 = # lax0, # buf0 = gndx0.flashsize, # lpt0 = # avol, # lpt1 = # avol, (elems nx ∪ dom gstore0) ++ n1 = dom gstore1 ∪ ginval, gstore1[n1] = groupblock(gndx1, lax1, m), avol[n1] = mapped(buf1), lpt1[n1] = mklp(m, # buf1, LP_GROUP_NODES, m3), keyset(gch) = gc-heap(lpt1, nx + n1 '), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, ginval ∩ elems nx = ∅, n1 < # avol, n0 < # lax0, ginval < # avol, n < gndx0.flashsize, abs-gstore(avol, lpt1, gstore1, ginval), abs-istore(avol, lpt1, istore2), abs-nodes(buf1, gndx1, lax1, # buf1 = LEB_SIZE), abs-nodes(subarray(buf0, 0, n), # buf1, prefixn(n0, gndx0), prefixn(n0, lax0), true), abs-nodes(buf0, # buf1, gndx0, lax0, false), awbuf-inv(avol, buffered(n1)), awbuf-inv(avol[n1, mapped(buf1 + subarray(buf0, 0, n))], buffered(n1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n1), lpt1, avol), bufs-log-only(buffered(n1), nx + n1 ', lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(gstore1 \ ginval), inv(gstore0), inv(istore2), inv(istore1), inv(groupblock(gndx1, lax1, m)), is-aligned(# buf1 + n, EB_PAGE_SIZE), log-group-block(nx + n1 ', lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, nx + n1 '), n1 ∈ gstore1, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore1 ⊑ istore2, ⌊err1⌋ , isbuf → synced(avol) ⊦ gndx0 = [], lax0 = [], n = 0, n0 = # lax0, dups(nx), n1 ∈ nx, n1 ∈ ginval, mapped(buf1 + subarray(buf0, 0, n)).mapped? ∧ abs-nodes (mapped(buf1 + subarray(buf0, 0, n)).data, groupblock(gndx1 + prefixn(n0, gndx0), lax1 + prefixn(n0, lax0), m).gndlist, groupblock(gndx1 + prefixn(n0, gndx0), lax1 + prefixn(n0, lax0), m).ladrlist, mklp(m, LEB_SIZE, LP_GROUP_NODES, m3).size = LEB_SIZE) ∧ ( mklp(m, LEB_SIZE, LP_GROUP_NODES, m3).size ≠ LEB_SIZE → mklp(m, LEB_SIZE, LP_GROUP_NODES, m3).size = # mapped(buf1 + subarray(buf0, 0, n)).data)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 226:
# lpt1 = # avol, # lpt0 = # avol, # buf0 = gndx0.flashsize, # gndx0 = # lax0, # gndx1 = # lax1, (elems nx ∪ dom gstore0) ++ n1 = dom gstore1 ∪ ginval, lpt1[n1] = mklp(m, # buf1, LP_GROUP_NODES, m3), avol[n1] = mapped(buf1), gstore1[n1] = groupblock(gndx1, lax1, m), keyset(gch) = gc-heap(lpt1, nx + n1 '), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, ginval ∩ elems nx = ∅, n < gndx0.flashsize, ginval < # avol, n0 < # lax0, n1 < # avol, abs-gstore(avol, lpt1, gstore1, ginval), abs-istore(avol, lpt1, istore2), abs-nodes(buf0, # buf1, gndx0, lax0, false), abs-nodes(subarray(buf0, 0, n), # buf1, prefixn(n0, gndx0), prefixn(n0, lax0), true), abs-nodes(buf1, gndx1, lax1, # buf1 = LEB_SIZE), awbuf-inv(avol[n1, mapped(buf1 + subarray(buf0, 0, n))], buffered(n1)), awbuf-inv(avol, buffered(n1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n1), lpt1, avol), bufs-log-only(buffered(n1), nx + n1 ', lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(groupblock(gndx1, lax1, m)), inv(istore1), inv(istore2), inv(gstore0), inv(gstore1 \ ginval), is-aligned(# buf1 + n, EB_PAGE_SIZE), log-group-block(nx + n1 ', lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, nx + n1 '), n1 ∈ gstore1, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore1 ⊑ istore2, ⌊err1⌋ , isbuf → synced(avol) ⊦ gndx0 = [], lax0 = [], n = 0, n0 = # lax0, abs-nodes(buf1 + subarray(buf0, 0, n), gndx1 + prefixn(n0, gndx0), lax1 + prefixn(n0, lax0), true), dups(nx), n1 ∈ ginval, n1 ∈ nx

Rule argument

Additional information

Used simplifier rules: ⊦ 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)