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Proof step 85 from proof inv-sync (previous step)

# lpt0 = # avol0, # lpt1 = # avol0, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, lpt1[n1] = mklp(m3, # buf, lpf, m4), avol0[n1] = mapped(buf), lpt1[n1] = mklp(m, m0, 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⌋ ⊦ ⟪awbuf_enter_readonly# (adr, m2, log0, avol0[buffered(n1).leb, mapped(avol0[buffered(n1).leb].data + subarray(buf1, 0, n))], lpt0, ns, buffered(n1); ; isbuf1)⟫ ( (lpf0 = LP_FREE → m = 0) ∧ freelist-cons(lpt1[n1, mklp(m, LEB_SIZE, lpf0, m1)], freelist) ∧ bin-heap-inv(gch, lpt1[n1, mklp(m, LEB_SIZE, lpf0, m1)]) ∧ keyset(gch) = gc-heap(lpt1[n1, mklp(m, LEB_SIZE, lpf0, m1)], log0) ∧ log-group-block(log0, lpt1[n1, mklp(m, LEB_SIZE, lpf0, m1)]) ∧ buf-ro-rw-mode(isbuf1, buffered(n1), lpt1[n1, mklp(m, LEB_SIZE, lpf0, m1)], avol0[n1, mapped(avol0[n1].data + subarray(buf1, 0, n))]) ∧ lpt-ram-flash(lpt1[n1, mklp(m, LEB_SIZE, lpf0, m1)], lpt0, log0)), buf1 = mkbuf(0), lpf = LP_FREE, n = 0, is-aligned(# buf, EB_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 86:
# lpt1 = # avol0, # lpt0 = # avol0, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, avol0[n1] = mapped(buf), lpt1[n1] = mklp(m, # buf, lpf0, m1), keyset(gch) = gc-heap(lpt1, log0), buf1 ≠ mkbuf(0), lpf0 ≠ LP_FREE, n ≠ 0, n < # buf1, n1 < # 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, ⌊err0⌋ , ¬ is-aligned(# buf, EB_PAGE_SIZE) ⊦ ⟪awbuf_enter_readonly# (adr, m2, log0, avol0[buffered(n1).leb, mapped(avol0[buffered(n1).leb].data + subarray(buf1, 0, n))], lpt0, ns, buffered(n1); ; isbuf1)⟫ ( keyset(gch) = gc-heap(lpt1[n1, mklp(m, LEB_SIZE, lpf0, m1)], log0) ∧ log-group-block(log0, lpt1[n1, mklp(m, LEB_SIZE, lpf0, m1)]) ∧ buf-ro-rw-mode(isbuf1, buffered(n1), lpt1[n1, mklp(m, LEB_SIZE, lpf0, m1)], avol0[n1, mapped(avol0[n1].data + subarray(buf1, 0, n))]))

Rule argument

Additional information

Used simplifier rules: ⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws)%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)%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 ↔ false); (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)