[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 153 from proof refine-add-gnds (previous step)

# gndx0 = # lax0, # buf0 = gndx0.flashsize, # lpt0 = # avol, # lpt1 = # avol, # gndx1 = # lax1, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, gstore[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 = ∅, ginval < # avol, n < # avol, abs-istore(avol, lpt1, istore2), abs-nodes(buf0, # buf1, gndx0, lax0, false), abs-nodes(buf1, gndx1, lax1, # buf1 = LEB_SIZE), 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), dups(lax1 + lax0), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(groupblock(gndx1, lax1, m1)), inv(gstore \ 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 ∈ gstore, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore1 ⊑ istore2, isbuf1 → synced(avol) ⊦ gndx0 = [], dups(nx), n ∈ nx, n ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 154:
⊦ abs-nodes(buf, gndx, lax, boolvar) → ¬ dups(lax)
Proof step 155:
# gndx1 = # lax1, # lpt1 = # avol, # lpt0 = # avol, # buf0 = gndx0.flashsize, # gndx0 = # lax0, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, lpt1[n] = mklp(m1, # buf1, LP_GROUP_NODES, m2), avol[n] = mapped(buf1), gstore[n] = groupblock(gndx1, lax1, m1), keyset(gch) = gc-heap(lpt1, nx + n '), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, ginval ∩ elems nx = ∅, n < # avol, ginval < # avol, abs-istore(avol, lpt1, istore2), abs-nodes(buf1, gndx1, lax1, # buf1 = LEB_SIZE), 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), dups(lax1 + lax0), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(istore1), inv(istore2), inv(gstore0), inv(gstore \ 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 ∈ gstore, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore1 ⊑ istore2, isbuf1 → synced(avol) ⊦ gndx0 = [], abs-nodes(buf1 + buf0, gndx1 + gndx0, lax1 + lax0, false), dups(nx), n ∈ ginval, n ∈ nx

Rule argument

spec: abs-list, inst: encoding-group-node name: abs-nodes-nodups seq: ⊦ abs-nodes(buf, gndx, lax, boolvar) → ¬ dups(lax) subst: [buf, gndx, boolvar, lax] → [buf1 + buf0, gndx1 + gndx0, false, lax1 + lax0] flags: <all paths>

Additional information

Used terms: buf1 + buf0, gndx1 + gndx0, false, lax1 + lax0