[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 40 from proof refine-sync (previous step)

# lpt0 = # avol, # lpt = # avol, istore[m2] = indexblock(indx, lax, m), lpt[m2] = mklp(m, m0, LP_INDEX_NODES, m1), keyset(gch) = gc-heap(lpt, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, m2 < # avol, ginval < # avol, abs-gstore(avol, lpt, gstore, ginval), awbuf-inv(avol, buffered(m2)), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, buffered(m2), lpt, avol), bufs-log-only(buffered(m2), log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), inv(indexblock(indx, lax, m)), log-group-block(log1, lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log1), m2 ∈ istore, istore0 ⊑ istore, isbuf → synced(avol), ∀ n. (n < # avol ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore) ∧ (n ∈ istore → abs-leb(avol[n], istore[n], lpt[n]) ∧ lpt[n].ref-size = istore[n].ref-size) ⊦ dups(log1), # avol[m2].data ≤ LEB_SIZE ∧ avol[m2].mapped? ∧ m0 = # avol[m2].data ∧ is-aligned(# avol[m2].data, 2 * NODE_HEADER_SIZE)

User applied rule all left

And obtained the following new goals

Proof step 41:
# lpt = # avol, # lpt0 = # avol, m2 < # avol ∧ lpt[m2].flags = LP_INDEX_NODES ↔ m2 ∈ istore, lpt[m2] = mklp(m, m0, LP_INDEX_NODES, m1), istore[m2] = indexblock(indx, lax, m), keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, m2 < # avol, abs-gstore(avol, lpt, gstore, ginval), awbuf-inv(avol, buffered(m2)), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, buffered(m2), lpt, avol), bufs-log-only(buffered(m2), log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(indexblock(indx, lax, m)), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log1), m2 ∈ istore, istore0 ⊑ istore, isbuf → synced(avol), m2 ∈ istore → abs-leb(avol[m2], istore[m2], lpt[m2]) ∧ lpt[m2].ref-size = istore[m2].ref-size ⊦ dups(log1), # avol[m2].data ≤ LEB_SIZE ∧ avol[m2].mapped? ∧ m0 = # avol[m2].data ∧ is-aligned(# avol[m2].data, 2 * NODE_HEADER_SIZE)

Rule argument

pos: left 33 terms: m2 abort: F discard: T computed: T

Additional information

Used terms: m2