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Proof step 164 from proof refine-add-gnds (previous step)

# lpt1 = # avol, # lpt0 = # avol, # buf0 = gndx0.flashsize, # gndx0 = # lax0, (elems nx ∪ dom gstore0) ++ n = dom gstore1 ∪ ginval, lpt1[n] = mklp(m1, # buf1, LP_GROUP_NODES, m2), avol[n] = mapped(buf1), gstore1[n] = groupblock(gndx1, lax1, m1), keyset(gch) = gc-heap(lpt1, nx + n '), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, ginval ∩ elems nx = ∅, ginval < # avol, n < # avol, abs-gstore(avol, lpt1, gstore1, ginval), abs-istore(avol, lpt1, istore2), abs-leb(mapped(buf1), groupblock(gndx1, lax1, m1), mklp(m1, # buf1, LP_GROUP_NODES, m2)), abs-nodes(buf0, # buf1, gndx0, lax0, false), awbuf-inv(avol, buffered(n)), awbuf-inv(avol[n, mapped(buf1 + buf0)], buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), nx + n ', lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(istore1), inv(istore2), inv(gstore0), inv(gstore1 \ ginval), inv(groupblock(gndx1, lax1, m1)), log-group-block(nx + n ', lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, nx + n '), n ∈ gstore1, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore1 ⊑ istore2, isbuf → synced(avol) ⊦ gndx0 = [], abs-leb(mapped(buf1 + buf0), groupblock(gndx1 + gndx0, lax1 + lax0, m1), mklp(m1, # buf1 + gndx0.flashsize, LP_GROUP_NODES, m2)), dups(nx), n ∈ ginval, n ∈ nx

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 165:
⊦ 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 166:
# gndx0 = # lax0, # buf0 = gndx0.flashsize, # lpt0 = # avol, # lpt1 = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore1 ∪ ginval, gstore1[n] = groupblock(gndx1, lax1, m1), avol[n] = mapped(buf1), lpt1[n] = mklp(m1, # buf1, LP_GROUP_NODES, m2), keyset(gch) = gc-heap(lpt1, nx + n '), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, ginval ∩ elems nx = ∅, n < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore1, ginval), abs-istore(avol, lpt1, istore2), abs-leb(mapped(buf1), groupblock(gndx1, lax1, m1), mklp(m1, # buf1, LP_GROUP_NODES, m2)), abs-nodes(buf0, # buf1, gndx0, lax0, false), awbuf-inv(avol[n, mapped(buf1 + buf0)], buffered(n)), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), nx + n ', lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(groupblock(gndx1, lax1, m1)), inv(gstore1 \ ginval), inv(gstore0), inv(istore2), inv(istore1), log-group-block(nx + n ', lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, nx + n '), n ∈ gstore1, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore1 ⊑ istore2, isbuf → synced(avol) ⊦ gndx0 = [], dups(nx), n ∈ nx, n ∈ ginval, mapped(buf1 + buf0).mapped? ∧ abs-nodes (mapped(buf1 + buf0).data, groupblock(gndx1 + gndx0, lax1 + lax0, m1).gndlist, groupblock(gndx1 + gndx0, lax1 + lax0, m1).ladrlist, mklp(m1, # buf1 + gndx0.flashsize, LP_GROUP_NODES, m2).size = LEB_SIZE) ∧ ( mklp(m1, # buf1 + gndx0.flashsize, LP_GROUP_NODES, m2).size ≠ LEB_SIZE → mklp(m1, # buf1 + gndx0.flashsize, LP_GROUP_NODES, m2).size = # mapped(buf1 + buf0).data)

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, # buf1 + gndx0.flashsize, LP_GROUP_NODES, m2), groupblock(gndx1 + gndx0, lax1 + lax0, m1), mapped(buf1 + buf0)] flags: <all paths>

Additional information

Used terms: mklp(m1, # buf1 + gndx0.flashsize, LP_GROUP_NODES, m2), groupblock(gndx1 + gndx0, lax1 + lax0, m1), mapped(buf1 + buf0)