[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 166 from proof refine-add-gnds (previous step)

# gndx0 = # lax0, # buf0 = gndx0.flashsize, # lpt0 = # avol, # lpt1 = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore1 ∪ ginval, gstore1[n] = groupblock(gndx1, lax1, m1), avol[n] = mapped(buf1), lpt1[n] = mklp(m1, # buf1, LP_GROUP_NODES, m2), keyset(gch) = gc-heap(lpt1, nx + n '), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, ginval ∩ elems nx = ∅, n < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore1, ginval), abs-istore(avol, lpt1, istore2), abs-leb(mapped(buf1), groupblock(gndx1, lax1, m1), mklp(m1, # buf1, LP_GROUP_NODES, m2)), abs-nodes(buf0, # buf1, gndx0, lax0, false), awbuf-inv(avol[n, mapped(buf1 + buf0)], buffered(n)), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), nx + n ', lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(groupblock(gndx1, lax1, m1)), inv(gstore1 \ ginval), inv(gstore0), inv(istore2), inv(istore1), log-group-block(nx + n ', lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, nx + n '), n ∈ gstore1, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore1 ⊑ istore2, isbuf → synced(avol) ⊦ gndx0 = [], dups(nx), n ∈ nx, n ∈ ginval, mapped(buf1 + buf0).mapped? ∧ abs-nodes (mapped(buf1 + buf0).data, groupblock(gndx1 + gndx0, lax1 + lax0, m1).gndlist, groupblock(gndx1 + gndx0, lax1 + lax0, m1).ladrlist, mklp(m1, # buf1 + gndx0.flashsize, LP_GROUP_NODES, m2).size = LEB_SIZE) ∧ ( mklp(m1, # buf1 + gndx0.flashsize, LP_GROUP_NODES, m2).size ≠ LEB_SIZE → mklp(m1, # buf1 + gndx0.flashsize, LP_GROUP_NODES, m2).size = # mapped(buf1 + buf0).data)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 167:
# lpt1 = # avol, # lpt0 = # avol, # buf0 = gndx0.flashsize, # gndx0 = # lax0, (elems nx ∪ dom gstore0) ++ n = dom gstore1 ∪ ginval, lpt1[n] = mklp(m1, # buf1, LP_GROUP_NODES, m2), avol[n] = mapped(buf1), gstore1[n] = groupblock(gndx1, lax1, m1), keyset(gch) = gc-heap(lpt1, nx + n '), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, ginval ∩ elems nx = ∅, ginval < # avol, n < # avol, abs-gstore(avol, lpt1, gstore1, ginval), abs-istore(avol, lpt1, istore2), abs-leb(mapped(buf1), groupblock(gndx1, lax1, m1), mklp(m1, # buf1, LP_GROUP_NODES, m2)), abs-nodes(buf0, # buf1, gndx0, lax0, false), awbuf-inv(avol, buffered(n)), awbuf-inv(avol[n, mapped(buf1 + buf0)], buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), nx + n ', lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(istore1), inv(istore2), inv(gstore0), inv(gstore1 \ ginval), inv(groupblock(gndx1, lax1, m1)), log-group-block(nx + n ', lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, nx + n '), n ∈ gstore1, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore1 ⊑ istore2, isbuf → synced(avol) ⊦ gndx0 = [], abs-nodes(buf1 + buf0, gndx1 + gndx0, lax1 + lax0, # buf1 + gndx0.flashsize = LEB_SIZE), dups(nx), n ∈ ginval, n ∈ nx

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)