Proof step 105 from proof refine-sync (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 106:

  # lpt0 = # avol0, # lpt1 = # avol0, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, lpt1[pstate.lnum] = mklp(m1, # buf0, lpf, m4), avol0[pstate.lnum] = mapped(buf0), avol = avol0[pstate.lnum, mapped(buf0 + buf1)], bleb1 = buffered(pstate.lnum), gc-heap(lpt1, log1) = gc-heap(lpt1[pstate.lnum, mklp(m1, # buf0 + (EB_PAGE_SIZE - # buf0 % EB_PAGE_SIZE), lpf, m4)], log1), ¬ isbuf, keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, buf1 ≠ mkbuf(0), lpf ≠ LP_FREE, pstate ≠ readonly, pstate ≠ unbuffered, ginval < # avol0, pstate.lnum < # avol0, abs-gstore(avol0, lpt1, gstore, ginval), abs-istore(avol0, lpt1, istore), abs-padding(buf1), awbuf-inv(avol0[pstate.lnum, mapped(buf0 + buf1)], buffered(pstate.lnum)), awbuf-inv(avol0, buffered(pstate.lnum)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt1, avol0), bufs-log-only(buffered(pstate.lnum), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), is-aligned(# buf0, 2 * NODE_HEADER_SIZE), log-group-block(log1, lpt1[pstate.lnum, mklp(m1, # buf0 + (EB_PAGE_SIZE - # buf0 % EB_PAGE_SIZE), lpf, m4)]), log-group-block(log1, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1[pstate.lnum, mklp(m1, # buf0 + (EB_PAGE_SIZE - # buf0 % EB_PAGE_SIZE), lpf, m4)], lpt0, log1), lpt-ram-flash(lpt1, lpt0, log1), EB_PAGE_SIZE + # buf0 ≤ LEB_SIZE + # buf0 % EB_PAGE_SIZE, # buf0 ≤ LEB_SIZE, # buf0 + # buf1 ≤ LEB_SIZE, istore0 ⊑ istore, ¬ dups(log1), ¬ is-aligned(# buf0, EB_PAGE_SIZE), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate.index? ∨ pstate.journal? ⊦ ⟨apersistence_sync#(adr0, istore, istore0, ginval, gstore, gstore0, log1, m2, ns0; pstate, isbuf; err1)⟩ ( abs-istore (avol, lpt1 [bleb1.leb, mklp (lpt1[bleb1.leb].ref-size, lpt1[bleb1.leb].size + (EB_PAGE_SIZE - # buf0 % EB_PAGE_SIZE), lpt1[bleb1.leb].flags, lpt1[bleb1.leb].gcheapidx) ], istore) ∧ abs-gstore (avol, lpt1 [bleb1.leb, mklp (lpt1[bleb1.leb].ref-size, lpt1[bleb1.leb].size + (EB_PAGE_SIZE - # buf0 % EB_PAGE_SIZE), lpt1[bleb1.leb].flags, lpt1[bleb1.leb].gcheapidx) ], gstore, ginval) ∧ (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb1 = nobuffer) ∧ pstate ≠ readonly ∧ (pstate ≠ unbuffered → bleb1 = buffered(pstate.lnum)) ∧ ESUCCESS = err1)

Rule argument

Additional information

Used simplifier rules: ⊦ freelist-cons(lpt, freelist) ∧ lpt[n] = mklp(m0, m1, lpf, m2) → freelist-cons(lpt[n, mklp(n0, n1, lpf, n2)], freelist); (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)% ⊦ m < n → n ≠ 0; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ EB_PAGE_SIZE = n0 + n1 → n0 + n1 + n2 = EB_PAGE_SIZE + n2; (s)% ⊦ mapped(buf).data = buf; (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% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ buffered(m).isbuf?; (s)% ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf)); (as)%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].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).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)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)% ⊦ mklp(n2, n3, lpf, m).size = n3; (s)%⊦ lpt-leb-size(lpt) → (lpt-leb-size(lpt[n, lp]) ↔ # lpt ≤ n ∨ lp.size ≤ LEB_SIZE); (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)% ⊦ # lpt[n, lp] = # lpt; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ buffered(m).leb = m; (s)