Proof step 55 from proof inv-sync (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 56:

  # lpt1 = # avol0, # lpt0 = # avol0, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, avol0[n] = mapped(buf0), lpt1[n] = mklp(m3, # buf0, lpf, m4), keyset(gch) = gc-heap(lpt1, log0), n < # avol0, abs-padding(buf1), awbuf-inv(avol0[n, mapped(buf0 + buf1)], buffered(n)), awbuf-inv(avol0, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol0), bufs-log-only(buffered(n), log0, lpt1), freelist-cons(lpt1, freelist), is-aligned(# buf0, 2 * NODE_HEADER_SIZE), log-group-block(log0, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log0), # buf0 ≤ LEB_SIZE, # buf0 + # buf1 ≤ LEB_SIZE ⊦ buf1 = mkbuf(0), lpf = LP_FREE, is-aligned(# buf0, EB_PAGE_SIZE), gc-heap(lpt1, log0) = gc-heap(lpt1[n, mklp(m3, # buf0 + (EB_PAGE_SIZE - # buf0 % EB_PAGE_SIZE), lpf, m4)], log0) ∧ log-group-block(log0, lpt1[n, mklp(m3, # buf0 + (EB_PAGE_SIZE - # buf0 % EB_PAGE_SIZE), lpf, m4)]) ∧ EB_PAGE_SIZE + # buf0 ≤ LEB_SIZE + # buf0 % EB_PAGE_SIZE

Rule argument

Additional information

Used simplifier rules: elim-mapped: ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf));%n < # lpt ⊦ bufs-log-only(buffered(n), nx, lpt) ∧ lpt-ram-flash(lpt, lpt0, nx) ∧ lpt[n] = mklp(n0, n1, lpf, n2) → lpt-ram-flash(lpt[n, mklp(m0, m1, lpf, m2)], lpt0, nx); (ss)% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ EB_PAGE_SIZE = n0 + n1 → n0 + n1 + n2 = EB_PAGE_SIZE + n2; (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)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%⊦ freelist-cons(lpt, freelist) ∧ lpt[n] = mklp(m0, m1, lpf, m2) → freelist-cons(lpt[n, mklp(n0, n1, lpf, n2)], freelist); (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)%inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)%⊦ lpt-leb-size(lpt) → (lpt-leb-size(lpt[n, lp]) ↔ # lpt ≤ n ∨ lp.size ≤ LEB_SIZE); (s)%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1; (s)%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, lp] = # 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)% ⊦ mklp(n2, n3, lpf, m).size = n3; (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)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ buffered(m).isbuf?; (s)% ⊦ m ≤ m; (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)%n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ # avol[n, aleb] = # avol; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ buffered(m).leb = m; (s)