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Proof step 131 from proof refine-add-ind (previous step)

# lpt0 = # avol, # buf1 = 2 * NODE_HEADER_SIZE + ind.alignedsize, # lpt1 = # avol, avol[m1] = mapped(buf0), lpt1[m1] = mklp(m4, # buf0, LP_INDEX_NODES, m2), istore[m1] = indexblock(indx, lax, m4), adr = @(pstate.lnum, # buf0, # buf1), err0 = ESUCCESS, keyset(gch) = gc-heap(lpt1, log1), pstate = index(m1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, m1 < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore2, ginval), abs-istore(avol, lpt1, istore), abs-node(buf1, ind), awbuf-inv(avol, buffered(m1)), awbuf-inv(avol[m1, mapped(buf0 + buf1)], buffered(m1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(m1), lpt1, avol), bufs-log-only(buffered(m1), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore1), freelist-cons(lpt1, freelist), inv(indexblock(indx, lax, m4)), inv(gstore2 \ ginval), inv(gstore1), inv(istore), inv(istore0), 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[m1, mklp(m4, # buf0 + # buf1, LP_INDEX_NODES, m2)], lpt0, log1), pstate.lnum ∈ istore, m1 ∈ istore, pstate.lnum ∈ istore[pstate.lnum, istore[pstate.lnum].indlist:= (istore[pstate.lnum].indlist + ind ')], # buf0 + # buf1 ≤ LEB_SIZE, istore0 ⊑ istore, isbuf → synced(avol), pstate.index? ∨ pstate.journal? ⊦ dups(log1), ∃ isbuf1. abs-istore (avol[pstate.lnum, mapped(avol[pstate.lnum].data + buf1)], lpt1[pstate.lnum, mklp(lpt1[pstate.lnum].ref-size, lpt1[pstate.lnum].size + # buf1, lpt1[pstate.lnum].flags, lpt1[pstate.lnum].gcheapidx)], istore[pstate.lnum, istore[pstate.lnum].indlist:= (istore[pstate.lnum].indlist + ind ')] [pstate.lnum, istore[pstate.lnum, istore[pstate.lnum].indlist:= (istore[pstate.lnum].indlist + ind ')][pstate.lnum] .ladrlist:= ( istore[pstate.lnum, istore[pstate.lnum].indlist:= (istore[pstate.lnum].indlist + ind ')][pstate.lnum].ladrlist + @(adr.pos, adr.size) ') ]) ∧ (isbuf1 → is-aligned(# avol[pstate.lnum].data + # buf1, EB_PAGE_SIZE)) ∧ pstate ≠ unbuffered ∧ pstate ≠ readonly ∧ m1 = pstate.lnum ∧ @(pstate.lnum, lpt1[pstate.lnum].size, # buf1) = adr ∧ ESUCCESS = err0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 132:
# lpt1 = # avol, # buf1 = 2 * NODE_HEADER_SIZE + ind.alignedsize, # lpt0 = # avol, istore[m1] = indexblock(indx, lax, m4), lpt1[m1] = mklp(m4, # buf0, LP_INDEX_NODES, m2), avol[m1] = mapped(buf0), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore1) = gstore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, ginval < # avol, m1 < # avol, abs-gstore(avol, lpt1, gstore2, ginval), abs-istore(avol, lpt1, istore), abs-leb(mapped(buf0), indexblock(indx, lax, m4), mklp(m4, # buf0, LP_INDEX_NODES, m2)), abs-node(buf1, ind), awbuf-inv(avol[m1, mapped(buf0 + buf1)], buffered(m1)), awbuf-inv(avol, buffered(m1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(m1), lpt1, avol), bufs-log-only(buffered(m1), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore1), freelist-cons(lpt1, freelist), inv(istore0), inv(istore), inv(gstore1), inv(gstore2 \ ginval), inv(indexblock(indx, lax, m4)), 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[m1, mklp(m4, # buf0 + # buf1, LP_INDEX_NODES, m2)], lpt0, log1), lpt-ram-flash(lpt1, lpt0, log1), m1 ∈ istore, # buf0 + # buf1 ≤ LEB_SIZE, istore0 ⊑ istore, isbuf → synced(avol) ⊦ abs-leb(mapped(buf0 + buf1), indexblock(indx + ind ', lax + @(# buf0, # buf1) ', m4), mklp(m4, # buf0 + # buf1, LP_INDEX_NODES, m2)), dups(log1)

Rule argument

Additional information

Used simplifier rules: ⊦ indexblock(indx, lax, m).ref-size = m; (s)%# lpt = # avol ⊦ abs-istore(avol, lpt, istore) → ( abs-istore(avol[n, aleb], lpt[n, lp], istore[n, iblock]) ↔ n < # lpt ∧ ( ( lpt[n].flags = LP_INDEX_NODES → lpt[n].ref-size = istore[n].ref-size) → lp.ref-size = iblock.ref-size ∧ lp.flags = LP_INDEX_NODES) ∧ ( ( lpt[n].flags = LP_INDEX_NODES → abs-leb(avol[n], istore[n], lpt[n])) → abs-leb(aleb, iblock, lp))); (ss)%⊦ indexblock(indx, lax, m).ladrlist:= lax0 = indexblock(indx, lax0, m); (s)% ⊦ indexblock(indx, lax, m).ladrlist = lax; (s)%⊦ indexblock(indx, lax, m).indlist:= indx0 = indexblock(indx0, lax, m); (s)% ⊦ indexblock(indx, lax, m).indlist = indx; (s)% ⊦ mklp(n2, n3, lpf, m).gcheapidx = m; (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ mklp(n2, n3, lpf, m).size = n3; (s)% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ readonly ≠ index(m); (s)% ⊦ unbuffered ≠ index(m); (s)% ⊦ istore[n, iblock][n, iblock0] = istore[n, iblock0]; (s)% ⊦ @(m, m0, m1).size = m1; (s)% ⊦ @(m, m0, m1).pos = m0; (s)% ⊦ (iblock.indlist:= indx).ladrlist = iblock.ladrlist; (s)% ⊦ istore[n, iblock][n] = iblock; (s)% ⊦ index(m).index?; (s)% ⊦ n ∈ istore[n, iblock]; (s)% ⊦ index(m).lnum = m; (s)