[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 15 from proof refine-read-gblock-nodes (previous step)

# lpt0 = # avol, # lpt = # avol, gstore[m] = groupblock(gndx1, lax, m1), lpt[m] = mklp(m1, m2, LP_GROUP_NODES, m3), keyset(gch) = gc-heap(lpt, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, m < # avol, ginval < # avol, abs-istore(avol, lpt, istore), abs-leb(avol[m], groupblock(gndx1, lax, m1), mklp(m1, m2, LP_GROUP_NODES, m3)), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(groupblock(gndx1, lax, m1)), 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), m ∈ gstore, istore0 ⊑ istore, pstate = unbuffered → isbuf, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer, isbuf → synced(avol) ⊦ dups(log1), m ∈ ginval, avol[m].mapped? ∧ (∃ gndx, lax. abs-nodes(avol[m].data, gndx, lax, true))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ abs-leb(aleb, gblock, lp) ↔ aleb.mapped? ∧ abs-nodes(aleb.data, gblock.gndlist, gblock.ladrlist, lp.size = LEB_SIZE) ∧ (lp.size ≠ LEB_SIZE → lp.size = # aleb.data)
Proof step 17:
# lpt = # avol, # lpt0 = # avol, lpt[m] = mklp(m1, m2, LP_GROUP_NODES, m3), gstore[m] = groupblock(gndx1, lax, m1), keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, avol[m].mapped?, ginval < # avol, m < # avol, abs-istore(avol, lpt, istore), abs-nodes(avol[m].data, groupblock(gndx1, lax, m1).gndlist, groupblock(gndx1, lax, m1).ladrlist, mklp(m1, m2, LP_GROUP_NODES, m3).size = LEB_SIZE), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), inv(groupblock(gndx1, lax, m1)), 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), m ∈ gstore, istore0 ⊑ istore, isbuf → synced(avol), pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate = unbuffered → isbuf, mklp(m1, m2, LP_GROUP_NODES, m3).size ≠ LEB_SIZE → mklp(m1, m2, LP_GROUP_NODES, m3).size = # avol[m].data ⊦ dups(log1), m ∈ ginval, avol[m].mapped? ∧ (∃ gndx, lax. abs-nodes(avol[m].data, gndx, lax, true))

Rule argument

spec: abs-leb, inst: encoding-group-node name: abs-leb-def seq: ⊦ abs-leb(aleb, gblock, lp) ↔ aleb.mapped? ∧ abs-nodes (aleb.data, gblock.gndlist, gblock.ladrlist, lp.size = LEB_SIZE) ∧ (lp.size ≠ LEB_SIZE → lp.size = # aleb.data) subst: [lp, gblock, aleb] → [mklp(m1, m2, LP_GROUP_NODES, m3), groupblock(gndx1, lax, m1), avol[m]] flags: <all paths>

Additional information

Used terms: mklp(m1, m2, LP_GROUP_NODES, m3), groupblock(gndx1, lax, m1), avol[m]