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Proof step 25 from proof refine-sync (previous step)

# lpt = # avol, # lpt0 = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, lpt[n] = mklp(m, m0, LP_GROUP_NODES, m1), gstore[n] = groupblock(gndx, lax, m), 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-leb(avol[n], groupblock(gndx, lax, m), mklp(m, m0, LP_GROUP_NODES, m1)), 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(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, istore0 ⊑ istore, isbuf → synced(avol) ⊦ dups(nx), n ∈ nx, n ∈ ginval, # avol[n].data ≤ LEB_SIZE ∧ avol[n].mapped? ∧ m0 = # avol[n].data ∧ is-aligned(# avol[n].data, 2 * NODE_HEADER_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ 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 27:
# lpt0 = # avol, # lpt = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, 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 = ∅, avol[n].mapped?, ginval < # avol, n < # avol, abs-istore(avol, lpt, istore), abs-nodes(avol[n].data, groupblock(gndx, lax, m).gndlist, groupblock(gndx, lax, m).ladrlist, mklp(m, m0, LP_GROUP_NODES, m1).size = 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, istore0 ⊑ istore, isbuf → synced(avol), mklp(m, m0, LP_GROUP_NODES, m1).size ≠ LEB_SIZE → mklp(m, m0, LP_GROUP_NODES, m1).size = # avol[n].data ⊦ dups(nx), n ∈ ginval, n ∈ nx, # avol[n].data ≤ LEB_SIZE ∧ avol[n].mapped? ∧ m0 = # avol[n].data ∧ is-aligned(# avol[n].data, 2 * NODE_HEADER_SIZE)

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(m, m0, LP_GROUP_NODES, m1), groupblock(gndx, lax, m), avol[n]] flags: <all paths>

Additional information

Used terms: mklp(m, m0, LP_GROUP_NODES, m1), groupblock(gndx, lax, m), avol[n]