[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 128 from proof refine-sync (previous step)

# lpt1 = # avol0, # lpt0 = # avol0, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, lpt1[pstate.lnum] = mklp(m1, # buf0, lpf, m4), avol0[pstate.lnum] = mapped(buf0), gc-heap(lpt1, log1) = gc-heap(lpt1[pstate.lnum, mklp(m1, # buf0 + # buf1, lpf, m4)], log1), keyset(gch) = gc-heap(lpt1, log1), lpf = LP_GROUP_NODES, remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, pstate.lnum < # avol0, ginval < # avol0, abs-gstore(avol0, lpt1, gstore2, ginval), abs-istore(avol0, lpt1, istore2), abs-padding(buf1), awbuf-inv(avol0, buffered(pstate.lnum)), awbuf-inv(avol0[pstate.lnum, mapped(buf0 + buf1)], buffered(pstate.lnum)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt1, avol0), bufs-log-only(buffered(pstate.lnum), log1, lpt1), flash-lpt-cons(lpt0, istore1, gstore1), freelist-cons(lpt1, freelist), inv(istore1), inv(istore2), inv(gstore1), inv(gstore2 \ ginval), is-aligned(# buf0, 2 * NODE_HEADER_SIZE), log-group-block(log1, lpt1), log-group-block(log1, lpt1[pstate.lnum, mklp(m1, # buf0 + # buf1, lpf, m4)]), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log1), lpt-ram-flash(lpt1[pstate.lnum, mklp(m1, # buf0 + # buf1, lpf, m4)], lpt0, log1), # buf0 + # buf1 ≤ LEB_SIZE, # buf0 ≤ LEB_SIZE, EB_PAGE_SIZE + # buf0 ≤ LEB_SIZE + # buf0 % EB_PAGE_SIZE, istore1 ⊑ istore2, pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? ∨ pstate.journal? ⊦ buf1 = mkbuf(0), lpf = LP_FREE, pstate = unbuffered, pstate = readonly, dups(log1), is-aligned(# buf0, EB_PAGE_SIZE), abs-istore(avol0[pstate.lnum, mapped(buf0 + buf1)], lpt1[pstate.lnum, mklp(m1, # buf0 + # buf1, lpf, m4)], istore2) ∧ abs-gstore(avol0[pstate.lnum, mapped(buf0 + buf1)], lpt1[pstate.lnum, mklp(m1, # buf0 + # buf1, lpf, m4)], gstore2, ginval)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 129:
# lpt0 = # avol0, # lpt1 = # avol0, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, avol0[pstate.lnum] = mapped(buf0), lpt1[pstate.lnum] = mklp(m1, # buf0, LP_GROUP_NODES, m4), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, ginval < # avol0, pstate.lnum < # avol0, abs-gstore(avol0, lpt1, gstore2, ginval), abs-istore(avol0, lpt1, istore2), abs-padding(buf1), awbuf-inv(avol0[pstate.lnum, mapped(buf0 + buf1)], buffered(pstate.lnum)), awbuf-inv(avol0, buffered(pstate.lnum)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt1, avol0), bufs-log-only(buffered(pstate.lnum), log1, lpt1), flash-lpt-cons(lpt0, istore1, gstore1), freelist-cons(lpt1, freelist), inv(gstore2 \ ginval), inv(gstore1), inv(istore2), inv(istore1), is-aligned(# buf0, 2 * NODE_HEADER_SIZE), log-group-block(log1, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1[pstate.lnum, mklp(m1, # buf0 + # buf1, LP_GROUP_NODES, m4)], lpt0, log1), lpt-ram-flash(lpt1, lpt0, log1), EB_PAGE_SIZE + # buf0 ≤ LEB_SIZE + # buf0 % EB_PAGE_SIZE, # buf0 ≤ LEB_SIZE, # buf0 + # buf1 ≤ LEB_SIZE, istore1 ⊑ istore2, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? → pstate.lnum ∈ istore2, pstate.index? ∨ pstate.journal? ⊦ buf1 = mkbuf(0), pstate = readonly, pstate = unbuffered, abs-gstore(avol0[pstate.lnum, mapped(buf0 + buf1)], lpt1[pstate.lnum, mklp(m1, # buf0 + # buf1, LP_GROUP_NODES, m4)], gstore2, ginval), dups(log1), is-aligned(# buf0, EB_PAGE_SIZE)

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)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ LP_GROUP_NODES ≠ LP_INDEX_NODES; (s)%n < # lpt ⊦ lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2) ∧ log-group-block(nx, lpt) → log-group-block(nx, lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)]); (s)% ⊦ LP_FREE ≠ LP_GROUP_NODES; (s)%n < # lpt ⊦ lpt[n] = mklp(m0, m1, LP_GROUP_NODES, m2) → gc-heap(lpt[n, mklp(m0, n1, LP_GROUP_NODES, n2)], nx) = gc-heap(lpt, nx); (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)