[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 228 from proof refine-sync (previous step)

# lpt1 = # avol0, # lpt0 = # avol0, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, lpt1[pstate.lnum, mklp(m, LEB_SIZE, LP_GROUP_NODES, m4)][n0] = mklp(m1, m2, lpf, m3), gstore2[n0] = groupblock(gndx, lax, m0), lpt1[pstate.lnum] = mklp(m, # buf, LP_GROUP_NODES, m4), avol0[pstate.lnum] = mapped(buf), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, pstate.lnum < # avol0, ginval < # avol0, n < # buf1, 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(buf + subarray(buf1, 0, n))], 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(# buf + n, EB_PAGE_SIZE), is-aligned(# buf, 2 * NODE_HEADER_SIZE), log-group-block(log1, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1[pstate.lnum, mklp(m, LEB_SIZE, LP_GROUP_NODES, m4)], lpt0, log1), lpt-ram-flash(lpt1, lpt0, log1), # buf + # buf1 ≤ LEB_SIZE, # buf ≤ LEB_SIZE, istore1 ⊑ istore2, ⌊err1⌋ , pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? ∨ pstate.journal? ⊦ buf1 = mkbuf(0), n = 0, pstate = readonly, pstate = unbuffered, dups(log1), is-aligned(# buf, EB_PAGE_SIZE), (n0 < # avol0 ∧ lpf = LP_GROUP_NODES ↔ n0 ∈ gstore2) ∧ ( n0 ∈ gstore2 ∧ ¬ n0 ∈ ginval → abs-leb(avol0[pstate.lnum, mapped(buf + subarray(buf1, 0, n))][n0], groupblock(gndx, lax, m0), mklp(m1, m2, lpf, m3))) ∧ (n0 ∈ gstore2 → m1 = m0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 229:
⊦ abs-gstore(avol, lpt, gstore, ginval) ↔ (∀ n. (n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size))
Proof step 230:
# lpt0 = # avol0, # lpt1 = # avol0, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, avol0[pstate.lnum] = mapped(buf), lpt1[pstate.lnum] = mklp(m, # buf, LP_GROUP_NODES, m4), gstore2[n0] = groupblock(gndx, lax, m0), lpt1[pstate.lnum, mklp(m, LEB_SIZE, LP_GROUP_NODES, m4)][n0] = mklp(m1, m2, lpf, m3), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, n < # buf1, ginval < # avol0, pstate.lnum < # avol0, abs-istore(avol0, lpt1, istore2), abs-padding(buf1), awbuf-inv(avol0[pstate.lnum, mapped(buf + subarray(buf1, 0, n))], 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(# buf, 2 * NODE_HEADER_SIZE), is-aligned(# buf + n, EB_PAGE_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, lpt0, log1), lpt-ram-flash(lpt1[pstate.lnum, mklp(m, LEB_SIZE, LP_GROUP_NODES, m4)], lpt0, log1), # buf ≤ LEB_SIZE, # buf + # buf1 ≤ LEB_SIZE, istore1 ⊑ istore2, ⌊err1⌋ , pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? → pstate.lnum ∈ istore2, ∀ n. (n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES ↔ n ∈ gstore2) ∧ (n ∈ gstore2 ∧ ¬ n ∈ ginval → abs-leb(avol0[n], gstore2[n], lpt1[n])) ∧ (n ∈ gstore2 → lpt1[n].ref-size = gstore2[n].ref-size), pstate.index? ∨ pstate.journal? ⊦ buf1 = mkbuf(0), n = 0, pstate = unbuffered, pstate = readonly, dups(log1), is-aligned(# buf, EB_PAGE_SIZE), (n0 < # avol0 ∧ lpf = LP_GROUP_NODES ↔ n0 ∈ gstore2) ∧ ( n0 ∈ gstore2 ∧ ¬ n0 ∈ ginval → abs-leb(avol0[pstate.lnum, mapped(buf + subarray(buf1, 0, n))][n0], groupblock(gndx, lax, m0), mklp(m1, m2, lpf, m3))) ∧ (n0 ∈ gstore2 → m1 = m0)

Rule argument

spec: persistence-base name: abs-gstore-def seq: ⊦ abs-gstore(avol, lpt, gstore, ginval) ↔ (∀ n. ( n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ ( n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size)) subst: [ginval, gstore, lpt, avol] → [ginval, gstore2, lpt1, avol0] flags: <all paths>

Additional information

Used terms: ginval, gstore2, lpt1, avol0