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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 132:

  # gndx0 = # lax0, # buf0 = gndx0.flashsize, # lpt0 = # avol, # lpt1 = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, avol[n] = mapped(buf1), lpt1[n] = mklp(m1, # buf1, LP_GROUP_NODES, m2), gstore[n] = groupblock(gndx, lax, m1), keyset(gch) = gc-heap(lpt1, nx + n '), pstate = journal(n), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, ginval ∩ elems nx = ∅, gndx0 ≠ [], ginval < # avol, n < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), abs-nodes(buf0, # buf1, gndx0, lax0, false), awbuf-inv(avol[n, mapped(buf1 + buf0)], buffered(n)), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), nx + n ', lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), inv(groupblock(gndx, lax, m1)), log-group-block(nx + n ', lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, nx + n '), n ∈ gstore, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore0 ⊑ istore, ¬ dups(nx), ¬ n ∈ ginval, ¬ n ∈ nx, isbuf1 → synced(avol) ⊦ ⟨apersistence_add_gnds#(gndx0, adr0, istore, istore0, ginval, gstore0, nx + n ', m0, ns0; ax0, gstore, pstate, isbuf1; err1)⟩ ( abs-gstore (avol[pstate.lnum, mapped(avol[pstate.lnum].data + buf0)], lpt1 [pstate.lnum, mklp(lpt1[pstate.lnum].ref-size, lpt1[pstate.lnum].size + gndx0.flashsize, lpt1[pstate.lnum].flags, lpt1[pstate.lnum].gcheapidx) ], gstore, ginval) ∧ (isbuf1 → is-aligned(# avol[pstate.lnum].data + # buf0, EB_PAGE_SIZE)) ∧ pstate ≠ unbuffered ∧ pstate ≠ readonly ∧ n = pstate.lnum ∧ lax0.to-adr(pstate.lnum) = ax0 ∧ ESUCCESS = err1)

Rule argument

Additional information

Used simplifier rules: ⊦ LP_FREE ≠ LP_GROUP_NODES; (s)% ⊦ m ≤ m; (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)%⊦ freelist-cons(lpt, freelist) ∧ lpt[n] = mklp(m0, m1, lpf, m2) → freelist-cons(lpt[n, mklp(n0, n1, lpf, n2)], freelist); (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)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (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; (ss)% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ mapped(buf).data = buf; (s)%inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv%⊦ awbuf-inv(avol, buffered(n)) → (synced(avol[n, mapped(buf)]) ↔ is-aligned(# buf, EB_PAGE_SIZE)); (s)%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_GROUP_NODES ≠ LP_INDEX_NODES; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ buffered(m).isbuf?; (s)% ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf)); (as)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)%n < # lpt, n < # avol ⊦ buf-ro-rw-mode (false, buffered(n), lpt[n, mklp(m0, m1, lpf, m2)], avol[n, mapped(buf)]) ↔ m1 = # buf; (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)% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)%⊦ lpt-free-unref(lpt) → ( lpt-free-unref(lpt[n, lp]) ↔ n < # lpt ∧ lp.flags = LP_FREE → lp.ref-size = 0); (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-ram-flash(lpt[n, lp], lpt0, nx + n ') ↔ lpt-ram-flash(lpt, lpt0, nx + n '); (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ nx + n ' ≠ []; (s)% ⊦ # avol[n, aleb] = # avol; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ # lpt[n, lp] = # lpt; (s)% ⊦ buffered(m).leb = m; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ (nx + n ').last = n; (s)