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Proof step 88 from proof inv-sync (previous step)

# lpt1 = # avol0, # lpt0 = # avol0, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, avol0[n1] = mapped(buf), lpt1[n1] = mklp(m0, # buf, lpf0, m1), avol = avol0[buffered(n1).leb, mapped(avol0[buffered(n1).leb].data + subarray(buf1, 0, n))], bleb = buffered(n1), keyset(gch) = gc-heap(lpt1, log0), log = log0, lpt = lpt0, m = m2, buffered(n1).isbuf?, avol0[buffered(n1).leb].mapped?, n < # buf1, n1 < # avol0, buffered(n1).leb < # avol0, abs-padding(buf1), awbuf-inv(avol0, buffered(n1)), awbuf-inv(avol0[n1, mapped(buf + subarray(buf1, 0, n))], buffered(n1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n1), lpt1, avol0), bufs-log-only(buffered(n1), log0, lpt1), freelist-cons(lpt1, freelist), is-aligned(# buf + n, EB_PAGE_SIZE), is-aligned(# buf, 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), # buf ≤ LEB_SIZE, # buf + # buf1 ≤ LEB_SIZE, 0 + n ≤ # buf1, ⌊err0⌋ ⊦ buf1 = mkbuf(0), lpf0 = LP_FREE, n = 0, is-aligned(# buf, EB_PAGE_SIZE), keyset(gch) = gc-heap(lpt1[n1, mklp(m0, LEB_SIZE, lpf0, m1)], log0) ∧ log-group-block(log0, lpt1[n1, mklp(m0, LEB_SIZE, lpf0, m1)]) ∧ buf-ro-rw-mode(true, buffered(n1), lpt1[n1, mklp(m0, LEB_SIZE, lpf0, m1)], avol0[n1, mapped(avol0[n1].data + subarray(buf1, 0, n))])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 89:
# lpt0 = # avol0, # lpt1 = # avol0, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, avol0[n1] = mapped(buf), lpt1[n1] = mklp(m0, # buf, lpf0, m1), keyset(gch) = gc-heap(lpt1, log0), n1 < # avol0, n < # buf1, abs-padding(buf1), awbuf-inv(avol0[n1, mapped(buf + subarray(buf1, 0, n))], buffered(n1)), awbuf-inv(avol0, buffered(n1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n1), lpt1, avol0), bufs-log-only(buffered(n1), log0, lpt1), freelist-cons(lpt1, freelist), is-aligned(# buf, 2 * NODE_HEADER_SIZE), is-aligned(# buf + n, EB_PAGE_SIZE), log-group-block(log0, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log0), # buf + # buf1 ≤ LEB_SIZE, # buf ≤ LEB_SIZE, ⌊err0⌋ ⊦ buf1 = mkbuf(0), lpf0 = LP_FREE, n = 0, is-aligned(# buf, EB_PAGE_SIZE), gc-heap(lpt1, log0) = gc-heap(lpt1[n1, mklp(m0, LEB_SIZE, lpf0, m1)], log0) ∧ log-group-block(log0, lpt1[n1, mklp(m0, LEB_SIZE, lpf0, m1)])

Rule argument

Additional information

Used simplifier rules: elim-mapped: ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf));% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)%⊦ buf-ro-rw-mode (true, buffered(n), lpt[n, mklp(m0, LEB_SIZE, lpf, m1)], avol) ↔ n < # lpt; (s)% ⊦ buffered(m).isbuf?; (s)% ⊦ buffered(m).leb = m; (s)% ⊦ m < n → m ≤ 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)