Proof step 232 from proof refine-add-ind (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 233:

  # lpt1 = # avol, # buf1 = 2 * NODE_HEADER_SIZE + ind.alignedsize, # lpt0 = # avol, avol[m1] = mapped(buf0), istore[m1] = indexblock(indx, lax, m4), lpt1[m1] = mklp(m4, # buf0, LP_INDEX_NODES, m2), adr = adr2, keyset(gch) = gc-heap(lpt1, log1), pstate = index(m1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, m1 < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), abs-node(buf1, ind), 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, gstore0), freelist-cons(lpt1, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ 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, lpt0, log1), lpt-ram-flash(lpt1[m1, mklp(m4, LEB_SIZE, LP_INDEX_NODES, m2)], lpt0, log1), m1 ∈ istore, # buf0 + # buf1 ≤ LEB_SIZE, istore0 ⊑ istore, ⌊err0⌋ , ¬ dups(log1), isbuf1 → synced(avol) ⊦ ⟨apersistence_add_ind#(ind, adr0, istore0, ginval, gstore, gstore0, log1, m0, ns0; adr2, istore, pstate, isbuf1; err1)⟩ ( abs-istore(avol, lpt1[m1, mklp(lpt1[m1].ref-size, LEB_SIZE, lpt1[m1].flags, lpt1[m1].gcheapidx)], istore) ∧ (isbuf1 → synced(avol)) ∧ pstate = readonly ∧ adr = adr2 ∧ err0 = err1)

Rule argument

Additional information

Used simplifier rules: ⊦ LP_FREE ≠ LP_INDEX_NODES; (s)%⊦ freelist-cons(lpt, freelist) ∧ lpt[n] = mklp(m0, m1, lpf, m2) → freelist-cons(lpt[n, mklp(n0, n1, lpf, n2)], freelist); (s)% ⊦ unbuffered ≠ readonly; (s)%lpf ≠ LP_GROUP_NODES, lp.flags ≠ LP_GROUP_NODES ⊦ lpt[n] = mklp(n0, n1, lpf, n2) → ( abs-gstore(avol, lpt[n, lp], gstore, ginval) ↔ abs-gstore(avol, lpt, gstore, ginval)); (s)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)% ⊦ buffered(m).isbuf?; (s)%lpf0 ≠ LP_GROUP_NODES, n < # lpt ⊦ lpt[n] = mklp(m0, m1, lpf0, m2) ∧ keyset(gch) = gc-heap(lpt, nx) → ( bin-heap-inv(gch, lpt[n, mklp(n0, n1, lpf1, n2)]) ↔ bin-heap-inv(gch, lpt)); (s)%⊦ buf-ro-rw-mode (true, buffered(n), lpt[n, mklp(m0, LEB_SIZE, lpf, m1)], avol) ↔ n < # lpt; (s)%lpt[n].flags = lp.flags ⊦ bufs-log-only(bleb, nx, lpt) → bufs-log-only(bleb, nx, lpt[n, lp]); (s)% ⊦ mklp(n2, n3, lpf, m).gcheapidx = m; (s)%n < # lpt, lpf ≠ LP_GROUP_NODES ⊦ lpt[n] = mklp(n0, n1, lpf, n2) ∧ log-group-block(nx, lpt) → log-group-block(nx, lpt[n, lp]); (s)% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)%⊦ lpt-free-unref(lpt) → ( lpt-free-unref(lpt[n, lp]) ↔ n < # lpt ∧ lp.flags = LP_FREE → lp.ref-size = 0); (s)% ⊦ m ≤ m; (s)% ⊦ mklp(n2, n3, lpf, m).size = n3; (s)%⊦ lpt-leb-size(lpt) → (lpt-leb-size(lpt[n, lp]) ↔ # lpt ≤ n ∨ lp.size ≤ LEB_SIZE); (s)% ⊦ # lpt[n, lp] = # lpt; (s)%lpf0 ≠ LP_GROUP_NODES, lpf1 ≠ LP_GROUP_NODES, n < # lpt ⊦ lpt[n] = mklp(m0, m1, lpf0, m2) → gc-heap(lpt[n, mklp(n0, n1, lpf1, n2)], nx) = gc-heap(lpt, nx); (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ LP_GROUP_NODES ≠ LP_INDEX_NODES; (s)% ⊦ buffered(m).leb = m; (s)