[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 42 from proof refine-deallocate-gnd (previous step)

# lpt2 = # avol, # lpt0 = # avol, lpt1[n].gcheapidx = lpt1[n].gcheapidx, lpt2[n] = mklp(m3, m1, LP_GROUP_NODES, m2), gstore[n] = groupblock(gndx, lax, m3), bh1 = gch, gch = gch, keyset(gch) = gc-heap(lpt2, log1), lpt1 = lpt2[n, mklp(0, 0, LP_FREE, m2)], lpt1 = lpt1, lpt3 = lpt1, m0 = n, n0 = lpt1[n].gcheapidx, natkey0 = m3, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, n < # avol, ginval < # avol, abs-gstore(avol, lpt2, gstore, ginval), abs-istore(avol, lpt2, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt2), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, bleb, lpt2, avol), bufs-log-only(bleb, log1, lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt0), lpt-leb-size(lpt2), lpt-leb-size(lpt0), lpt-ram-flash(lpt2, lpt0, log1), synced(avol), n ∈ gstore, n ∈ gstore0, key-index(m3, n) ∈ gc-heap(lpt2, log1), key-index(m3, n) ∈ keyset(gch), istore0 ⊑ istore, pstate ≠ unbuffered → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore ⊦ [gc_heap_remove#(lpt1[n].gcheapidx; gch, lpt1)] ( bin-heap-inv(gch, lpt1) ∧ id-idx(lpt3, lpt1) ∧ keyset(gch) = keyset(bh1) -- key-index(natkey0, m0) → ⟪err := ESUCCESS⟫ ⟨apersistence_deallocate_gnd#(n, adr0, istore, istore0, gstore0, log1, m, ns0, pstate, true; ginval, gstore; err0)⟩ ( abs-istore(avol[n, unmapped], lpt1, istore) ∧ abs-gstore(avol[n, unmapped], lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered → bleb = buffered(pstate.lnum)) ∧ err = err0)), # gc-heap(lpt2, log1) = 0, buffered(n) = bleb, gc-heap(lpt2, log1) = ∅, pstate = readonly, dups(log1), n ∈ log1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
# lpt2 = # avol, # lpt0 = # avol, lpt2[n] = mklp(m3, m1, LP_GROUP_NODES, m2), gstore[n] = groupblock(gndx, lax, m3), bh1 = gch, keyset(gch) = gc-heap(lpt2, log1), lpt1 = lpt2[n, mklp(0, 0, LP_FREE, m2)], remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, # gc-heap(lpt2, log1) ≠ 0, buffered(n) ≠ bleb, gc-heap(lpt2, log1) ≠ ∅, pstate ≠ readonly, n < # avol, ginval < # avol, abs-gstore(avol, lpt2, gstore, ginval), abs-istore(avol, lpt2, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb, lpt2, avol), bufs-log-only(bleb, log1, lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt0), lpt-leb-size(lpt2), lpt-leb-size(lpt0), lpt-ram-flash(lpt2, lpt0, log1), synced(avol), n ∈ gstore, n ∈ gstore0, key-index(m3, n) ∈ gc-heap(lpt2, log1), istore0 ⊑ istore, ¬ dups(log1), ¬ n ∈ log1, pstate ≠ unbuffered → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore ⊦ [gc_heap_remove#(lpt1[n].gcheapidx; gch, lpt1)] ( bin-heap-inv(gch, lpt1) ∧ id-idx(lpt2[n, mklp(0, 0, LP_FREE, m2)], lpt1) ∧ keyset(gch) = keyset(bh1) -- key-index(m3, n) → ⟪err := ESUCCESS⟫ ⟨apersistence_deallocate_gnd#(n, adr0, istore, istore0, gstore0, log1, m, ns0, pstate, true; ginval, gstore; err0)⟩ ( abs-gstore(avol[n, unmapped], lpt2[n, mklp(0, 0, LP_FREE, m2)], gstore, ginval) ∧ ginval < # lpt1 ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered → bleb = buffered(pstate.lnum)) ∧ err = err0))

Rule argument

Additional information

Used simplifier rules: lpf ≠ LP_INDEX_NODES ⊦ lpt[n] = mklp(n0, n1, lpf, n2) → ( abs-istore(avol[n, aleb], lpt, istore) ↔ abs-istore(avol, lpt, istore)); (s)%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)% ⊦ LP_FREE ≠ LP_INDEX_NODES; (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)