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Proof step 28 from proof refine-sync (previous step)

# gndx = # lax, # lpt0 = # avol, # lpt = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, avol[n] = mapped(buf), gstore[n] = groupblock(gndx, lax, m), lpt[n] = mklp(m, m0, LP_GROUP_NODES, m1), keyset(gch) = gc-heap(lpt, nx + n '), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, ginval ∩ elems nx = ∅, ginval < # avol, n < # avol, abs-istore(avol, lpt, istore), abs-nodes(buf, gndx, lax, m0 = LEB_SIZE), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, buffered(n), lpt, avol), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), inv(groupblock(gndx, lax, m)), log-group-block(nx + n ', lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, nx + n '), n ∈ gstore, # buf ≤ LEB_SIZE, istore0 ⊑ istore, isbuf → synced(avol), m0 ≠ LEB_SIZE → m0 = # buf ⊦ dups(nx), n ∈ ginval, n ∈ nx, is-aligned(# buf, 2 * NODE_HEADER_SIZE) ∧ m0 = # buf

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ buf-ro-rw-mode(boolvar, bleb, lpt, avol) ↔ bleb.isbuf? → bleb.leb < # lpt ∧ (boolvar ∧ lpt[bleb.leb].size = LEB_SIZE ∨ lpt[bleb.leb].size = # avol[bleb.leb].data)
Proof step 30:
# lpt = # avol, # lpt0 = # avol, # gndx = # lax, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, lpt[n] = mklp(m, m0, LP_GROUP_NODES, m1), gstore[n] = groupblock(gndx, lax, m), avol[n] = mapped(buf), keyset(gch) = gc-heap(lpt, nx + n '), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, ginval ∩ elems nx = ∅, n < # avol, ginval < # avol, abs-istore(avol, lpt, istore), abs-nodes(buf, gndx, lax, m0 = LEB_SIZE), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(groupblock(gndx, lax, m)), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(nx + n ', lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, nx + n '), n ∈ gstore, # buf ≤ LEB_SIZE, istore0 ⊑ istore, m0 ≠ LEB_SIZE → m0 = # buf, isbuf → synced(avol), buffered(n).isbuf? → buffered(n).leb < # lpt ∧ (false ∧ lpt[buffered(n).leb].size = LEB_SIZE ∨ lpt[buffered(n).leb].size = # avol[buffered(n).leb].data) ⊦ dups(nx), n ∈ nx, n ∈ ginval, is-aligned(# buf, 2 * NODE_HEADER_SIZE) ∧ m0 = # buf

Rule argument

spec: persistence-base name: buf-ro-rw-mode seq: ⊦ buf-ro-rw-mode(boolvar, bleb, lpt, avol) ↔ bleb.isbuf? → bleb.leb < # lpt ∧ ( boolvar ∧ lpt[bleb.leb].size = LEB_SIZE ∨ lpt[bleb.leb].size = # avol[bleb.leb].data) subst: [avol, lpt, bleb, boolvar] → [avol, lpt, buffered(n), false] flags: <all paths>

Additional information

Used terms: avol, lpt, buffered(n), false