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Proof step 78 from proof inv-sync (previous step)

# lpt0 = # avol, # lpt0 = # avol0, # lpt1 = # avol0, isbuf1 ↔ true, isbuf ↔ false, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, avol0[n1] = mapped(buf), lpt1[n1] = mklp(m3, # buf, lpf, m4), avol = avol0[m, mapped(avol0[m].data + subarray(buf0, 0, n))], bleb1 = buffered(n1), buf0 = buf1, err = err0, keyset(gch) = gc-heap(lpt1, log0), m = buffered(n1).leb, m0 = EB_PAGE_SIZE - lpt1[buffered(n1).leb].size % EB_PAGE_SIZE, n0 = # buf1, buffered(n1).isbuf?, avol0[m].mapped?, buffered(n1).leb < # lpt1, m < # avol0, n < n0, n1 < # avol0, abs-padding(buf1), awbuf-inv(avol, 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(# avol0[m].data + n, EB_PAGE_SIZE), is-aligned(# buf, 2 * NODE_HEADER_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), 0 + n ≤ # buf0, # buf + # buf1 ≤ LEB_SIZE, # buf ≤ LEB_SIZE, EB_PAGE_SIZE ≥ lpt1[buffered(n1).leb].size % EB_PAGE_SIZE, n ≠ 0 → n < n0 → avol0[m].mapped? ∧ m < # avol0, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪debug#("persistence: flushing of LEB " + bleb1.leb.toString + " failed"); lpt1[bleb1.leb] := mklp(lpt1[bleb1.leb].ref-size, LEB_SIZE, lpt1[bleb1.leb].flags, lpt1[bleb1.leb].gcheapidx); awbuf_enter_readonly#(adr, m2, log0, avol, lpt0, ns, bleb1; ; isbuf1)⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(bleb1, log0, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf1, bleb1, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0) ∧ awbuf-inv(avol, bleb1)), EB_PAGE_SIZE = 0, buf1 = mkbuf(0), err = ESUCCESS, lpf = LP_FREE, n = 0, is-aligned(# buf, EB_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 79:
# lpt1 = # avol0, # lpt0 = # avol0, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, avol0[n1] = mapped(buf), lpt1[n1] = mklp(m3, # buf, lpf, m4), keyset(gch) = gc-heap(lpt1, log0), buf1 ≠ mkbuf(0), lpf ≠ 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) ⊦ ⟪debug#("persistence: flushing of LEB " + buffered(n1).leb.toString + " failed"); lpt1[buffered(n1).leb] := mklp(lpt1[buffered(n1).leb].ref-size, LEB_SIZE, lpt1[buffered(n1).leb].flags, lpt1[buffered(n1).leb].gcheapidx); 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)⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(buffered(n1), log0, lpt1) ∧ # lpt1 = # avol0 ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf1, buffered(n1), lpt1, avol0[n1, mapped(avol0[n1].data + subarray(buf1, 0, n))]) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0))

Rule argument

Additional information

Used simplifier rules: elim-mapped: ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf));% ⊦ mapped(buf).data = buf; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (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%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)% ⊦ buffered(m).isbuf?; (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)%n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ # avol[n, aleb] = # avol; (s)% ⊦ buffered(m).leb = m; (s)