Proof step 179 from proof refine-add-gnds (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 180:

  # gndx0 = # lax0, # buf0 = gndx0.flashsize, # lpt0 = # avol, # lpt1 = # avol, (elems nx ∪ dom gstore0) ++ n1 = dom gstore ∪ ginval, avol[n1] = mapped(buf1), lpt1[n1] = mklp(m1, # buf1, LP_GROUP_NODES, m2), gstore[n1] = groupblock(gndx, lax, m1), keyset(gch) = gc-heap(lpt1, nx + n1 '), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, ginval ∩ elems nx = ∅, gndx0 ≠ [], n ≠ 0, ginval < # avol, n1 < # avol, n < gndx0.flashsize, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), abs-nodes(buf0, # buf1, gndx0, lax0, false), awbuf-inv(avol, buffered(n1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n1), lpt1, avol), bufs-log-only(buffered(n1), nx + n1 ', 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)), is-aligned(# buf1 + n, EB_PAGE_SIZE), log-group-block(nx + n1 ', lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, nx + n1 '), n1 ∈ gstore, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore0 ⊑ istore, ⌊err0⌋ , ¬ dups(nx), ¬ n1 ∈ ginval, ¬ n1 ∈ nx, isbuf1 → synced(avol) ⊦ [debug#("persistence: adding group node to LEB " + buffered((nx + n1 ').last).leb.toString + " failed"); lpt1[buffered((nx + n1 ').last).leb] := mklp (lpt1[buffered((nx + n1 ').last).leb].ref-size, LEB_SIZE, lpt1[buffered((nx + n1 ').last).leb].flags, lpt1[buffered((nx + n1 ').last).leb].gcheapidx)] ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, nx + n1 ') ∧ bufs-log-only(buffered(n1), nx + n1 ', lpt1) ∧ # lpt1 = # avol ∧ log-group-block(nx + n1 ', lpt1) ∧ buf-ro-rw-mode(true, buffered(n1), lpt1, avol[n1, mapped(avol[n1].data + subarray(buf0, 0, n))]) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, nx + n1 ') ∧ awbuf-inv(avol[n1, mapped(avol[n1].data + subarray(buf0, 0, n))], buffered(n1)) → ⟨pstate := journal((nx + n1 ').last); apersistence_add_gnds#(gndx0, adr0, istore, istore0, ginval, gstore0, nx + n1 ', m0, ns0; ax0, gstore, pstate, isbuf1; err1)⟩ ( abs-istore(avol[n1, mapped(avol[n1].data + subarray(buf0, 0, n))], lpt1, istore) ∧ abs-gstore(avol[n1, mapped(avol[n1].data + subarray(buf0, 0, n))], lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ pstate = readonly ∧ lax0.to-adr(n1) = ax0 ∧ err0 = err1))

Rule argument

Additional information

Used simplifier rules: fwd-in-gstore-lpt: ⊦ n ∈ gstore ∧ abs-gstore(avol, lpt, gstore, ginval) → n < # lpt ∧ lpt[n].ref-size = gstore[n].ref-size ∧ lpt[n].flags = LP_GROUP_NODES;% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ groupblock(gndx, lax, m).ref-size = m; (s)% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)% ⊦ m < n → m ≤ n; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ gndx.flashsize = 0 ↔ gndx = []; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)%inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ unbuffered ≠ readonly; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%⊦ awbuf-inv(avol, buffered(n)) → (synced(avol[n, mapped(buf)]) ↔ is-aligned(# buf, EB_PAGE_SIZE)); (s)% ⊦ # avol[n, aleb] = # avol; (s)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)% ⊦ buffered(m).isbuf?; (s)% ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf)); (as)% ⊦ buffered(m).leb = m; (s)% ⊦ (nx + n ').last = 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)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ nx + n ' ≠ []; (s)