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Proof step 19 from proof refine-sync (previous step)

# lpt = # avol, # lpt0 = # avol, lpt[log1.last] = mklp(m, m0, LP_GROUP_NODES, m1), gstore[log1.last] = groupblock(gndx, 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, log1.last < # avol, ginval < # avol, abs-istore(avol, lpt, istore), awbuf-inv(avol, buffered(log1.last)), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, buffered(log1.last), lpt, avol), bufs-log-only(buffered(log1.last), log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), inv(groupblock(gndx, lax, m)), 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), log1.last ∈ gstore, istore0 ⊑ istore, ¬ log1.last ∈ ginval → abs-leb(avol[log1.last], groupblock(gndx, lax, m), mklp(m, m0, LP_GROUP_NODES, m1)), isbuf → synced(avol) ⊦ log1 = [], dups(log1), # avol[log1.last].data ≤ LEB_SIZE ∧ avol[log1.last].mapped? ∧ m0 = # avol[log1.last].data ∧ is-aligned(# avol[log1.last].data, 2 * NODE_HEADER_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ bufs-log-only(bleb, nx, lpt) ↔ bleb = nobuffer ∨ bleb.leb < # lpt ∧ (nx ≠ [] ∧ bleb.leb = nx.last ∧ lpt[bleb.leb].flags = LP_GROUP_NODES ∨ lpt[bleb.leb].flags = LP_INDEX_NODES)
Proof step 21:
# lpt0 = # avol, # lpt = # avol, gstore[log1.last] = groupblock(gndx, lax, m), lpt[log1.last] = mklp(m, m0, LP_GROUP_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, ginval < # avol, log1.last < # avol, abs-istore(avol, lpt, istore), awbuf-inv(avol, buffered(log1.last)), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, buffered(log1.last), lpt, avol), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(groupblock(gndx, lax, m)), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), 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), log1.last ∈ gstore, istore0 ⊑ istore, isbuf → synced(avol), ¬ log1.last ∈ ginval → abs-leb(avol[log1.last], groupblock(gndx, lax, m), mklp(m, m0, LP_GROUP_NODES, m1)), buffered(log1.last) = nobuffer ∨ buffered(log1.last).leb < # lpt ∧ ( log1 ≠ [] ∧ buffered(log1.last).leb = log1.last ∧ lpt[buffered(log1.last).leb].flags = LP_GROUP_NODES ∨ lpt[buffered(log1.last).leb].flags = LP_INDEX_NODES) ⊦ log1 = [], dups(log1), # avol[log1.last].data ≤ LEB_SIZE ∧ avol[log1.last].mapped? ∧ m0 = # avol[log1.last].data ∧ is-aligned(# avol[log1.last].data, 2 * NODE_HEADER_SIZE)

Rule argument

spec: persistence-base name: bufs-log-only seq: ⊦ bufs-log-only(bleb, nx, lpt) ↔ bleb = nobuffer ∨ bleb.leb < # lpt ∧ ( nx ≠ [] ∧ bleb.leb = nx.last ∧ lpt[bleb.leb].flags = LP_GROUP_NODES ∨ lpt[bleb.leb].flags = LP_INDEX_NODES) subst: [lpt, nx, bleb] → [lpt, log1, buffered(log1.last)] flags: <all paths>

Additional information

Used terms: lpt, log1, buffered(log1.last)