[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 17 from proof refine-set-gblock-refsize (previous step)

# lpt1 = # avol, # lpt0 = # avol, lpt[m].gcheapidx = lpt[m].gcheapidx, lpt1[m] = mklp(m1, m2, LP_GROUP_NODES, m3), gstore[m] = groupblock(gndx, lax, m1), bh1 = gch, gch = gch, keyset(gch) = gc-heap(lpt1, log0), lpt = lpt1[m, mklp(n, m2, LP_GROUP_NODES, m3)], lpt = lpt, lpt2 = lpt, m4 = m, n0 = lpt[m].gcheapidx, natkey1 = m1, natkey2 = n, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log0 ∩ ginval = ∅, dom gstore0 ∪ elems log0 = dom gstore ∪ ginval, m < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt1), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt1, avol), bufs-log-only(bleb, log0, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log0, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log0), m ∈ gstore0, m ∈ gstore, key-index(m1, m) ∈ gc-heap(lpt1, log0), key-index(m1, m) ∈ keyset(gch), istore0 ⊑ istore, isbuf → synced(avol), pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log0 ≠ [] ∧ pstate.lnum = log0.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate = unbuffered → isbuf ⊦ [gc_heap_update#(lpt[m].gcheapidx, n; gch, lpt)] ( bin-heap-inv(gch, lpt) ∧ id-idx(lpt2, lpt) ∧ keyset(gch) = (keyset(bh1) -- key-index(natkey1, m4)) ++ key-index(natkey2, m4) → ⟨apersistence_set_gblock_refsize#(m, n, adr0, istore, istore0, ginval, gstore0, log0, m0, ns0, pstate, isbuf; gstore)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ ginval < # lpt ∧ (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)))), # gc-heap(lpt1, log0) = 0, gc-heap(lpt1, log0) = ∅, dups(log0), m ∈ log0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
# lpt1 = # avol, # lpt0 = # avol, lpt1[m] = mklp(m1, m2, LP_GROUP_NODES, m3), gstore[m] = groupblock(gndx, lax, m1), bh1 = gch, keyset(gch) = gc-heap(lpt1, log0), lpt = lpt1[m, mklp(n, m2, LP_GROUP_NODES, m3)], remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log0 ∩ ginval = ∅, dom gstore0 ∪ elems log0 = dom gstore ∪ ginval, # gc-heap(lpt1, log0) ≠ 0, gc-heap(lpt1, log0) ≠ ∅, m < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(pstate = readonly, bleb, lpt1, avol), bufs-log-only(bleb, log0, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log0, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log0), m ∈ gstore0, m ∈ gstore, key-index(m1, m) ∈ gc-heap(lpt1, log0), istore0 ⊑ istore, ¬ dups(log0), ¬ m ∈ log0, isbuf → synced(avol), pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log0 ≠ [] ∧ pstate.lnum = log0.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate = unbuffered → isbuf ⊦ [gc_heap_update#(lpt[m].gcheapidx, n; gch, lpt)] ( bin-heap-inv(gch, lpt) ∧ id-idx(lpt1[m, mklp(n, m2, LP_GROUP_NODES, m3)], lpt) ∧ keyset(gch) = (keyset(bh1) -- key-index(m1, m)) ++ key-index(n, m) → ⟨apersistence_set_gblock_refsize#(m, n, adr0, istore, istore0, ginval, gstore0, log0, m0, ns0, pstate, isbuf; gstore)⟩ ( abs-gstore(avol, lpt1[m, mklp(n, m2, LP_GROUP_NODES, m3)], gstore, ginval) ∧ ginval < # lpt ∧ (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum))))

Rule argument

Additional information

Used simplifier rules: lpf ≠ LP_INDEX_NODES, lp.flags ≠ LP_INDEX_NODES ⊦ lpt[n] = mklp(n0, n1, lpf, n2) → ( abs-istore(avol, lpt[n, lp], istore) ↔ abs-istore(avol, lpt, istore)); (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ LP_GROUP_NODES ≠ LP_INDEX_NODES; (s)%⊦ id-idx(lpt0, lpt1) → ( abs-gstore(avol, lpt1, gstore, ginval) ↔ abs-gstore(avol, lpt0, gstore, ginval)); (s)%⊦ id-idx(lpt0, lpt1) → (abs-istore(avol, lpt1, istore) ↔ abs-istore(avol, lpt0, istore)); (s)%n < # lpt ⊦ lpt[n] = mklp(m0, m1, lpf0, m2) → ( bin-heap-inv(gch, lpt[n, mklp(n0, n1, lpf1, m2)]) ↔ bin-heap-inv(gch, lpt)); (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)