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Proof step 191 from proof refine-sync (previous step)

# lpt0 = # avol0, # lpt1 = # avol0, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, lpt1[pstate.lnum] = mklp(m1, # buf, lpf, m4), avol0[pstate.lnum] = mapped(buf), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, buffered(pstate.lnum).isbuf?, buffered(pstate.lnum).leb < # lpt1, pstate.lnum < # avol0, n < # buf1, ginval < # avol0, abs-gstore(avol0, lpt1, gstore, ginval), abs-istore(avol0, lpt1, istore), abs-padding(buf1), 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(# buf, 2 * NODE_HEADER_SIZE), is-aligned(# buf + n, EB_PAGE_SIZE), 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, lpt0, log1), # buf ≤ LEB_SIZE, # buf + # buf1 ≤ LEB_SIZE, istore0 ⊑ istore, ⌊err0⌋ , pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate.index? ∨ pstate.journal? ⊦ [awbuf_enter_readonly# (adr0, m2, log1, avol0[buffered(pstate.lnum).leb, mapped(avol0[buffered(pstate.lnum).leb].data + subarray(buf1, 0, n))], lpt0, ns0, buffered(pstate.lnum) ; ; isbuf2)] ( lpt-free-unref (lpt1 [buffered(pstate.lnum).leb, mklp(lpt1[buffered(pstate.lnum).leb].ref-size, LEB_SIZE, lpt1[buffered(pstate.lnum).leb].flags, lpt1[buffered(pstate.lnum).leb].gcheapidx) ]) ∧ freelist-cons (lpt1 [buffered(pstate.lnum).leb, mklp(lpt1[buffered(pstate.lnum).leb].ref-size, LEB_SIZE, lpt1[buffered(pstate.lnum).leb].flags, lpt1[buffered(pstate.lnum).leb].gcheapidx) ], freelist) ∧ bin-heap-inv (gch, lpt1 [buffered(pstate.lnum).leb, mklp(lpt1[buffered(pstate.lnum).leb].ref-size, LEB_SIZE, lpt1[buffered(pstate.lnum).leb].flags, lpt1[buffered(pstate.lnum).leb].gcheapidx) ]) ∧ keyset(gch) = gc-heap (lpt1 [buffered(pstate.lnum).leb, mklp (lpt1[buffered(pstate.lnum).leb].ref-size, LEB_SIZE, lpt1[buffered(pstate.lnum).leb].flags, lpt1[buffered(pstate.lnum).leb].gcheapidx) ], log1) ∧ bufs-log-only (buffered(pstate.lnum), log1, lpt1 [buffered(pstate.lnum).leb, mklp(lpt1[buffered(pstate.lnum).leb].ref-size, LEB_SIZE, lpt1[buffered(pstate.lnum).leb].flags, lpt1[buffered(pstate.lnum).leb].gcheapidx) ]) ∧ # lpt1 [buffered(pstate.lnum).leb, mklp (lpt1[buffered(pstate.lnum).leb].ref-size, LEB_SIZE, lpt1[buffered(pstate.lnum).leb].flags, lpt1[buffered(pstate.lnum).leb].gcheapidx) ] = # avol0 ∧ log-group-block (log1, lpt1 [buffered(pstate.lnum).leb, mklp(lpt1[buffered(pstate.lnum).leb].ref-size, LEB_SIZE, lpt1[buffered(pstate.lnum).leb].flags, lpt1[buffered(pstate.lnum).leb].gcheapidx) ]) ∧ buf-ro-rw-mode (isbuf2, buffered(pstate.lnum), lpt1 [buffered(pstate.lnum).leb, mklp(lpt1[buffered(pstate.lnum).leb].ref-size, LEB_SIZE, lpt1[buffered(pstate.lnum).leb].flags, lpt1[buffered(pstate.lnum).leb].gcheapidx) ], avol0[pstate.lnum, mapped(avol0[pstate.lnum].data + subarray(buf1, 0, n))]) ∧ lpt-leb-size (lpt1 [buffered(pstate.lnum).leb, mklp(lpt1[buffered(pstate.lnum).leb].ref-size, LEB_SIZE, lpt1[buffered(pstate.lnum).leb].flags, lpt1[buffered(pstate.lnum).leb].gcheapidx) ]) ∧ lpt-ram-flash (lpt1 [buffered(pstate.lnum).leb, mklp(lpt1[buffered(pstate.lnum).leb].ref-size, LEB_SIZE, lpt1[buffered(pstate.lnum).leb].flags, lpt1[buffered(pstate.lnum).leb].gcheapidx) ], lpt0, log1) ∧ awbuf-inv(avol0[pstate.lnum, mapped(avol0[pstate.lnum].data + subarray(buf1, 0, n))], buffered(pstate.lnum)) → ⟨isbuf1 := false; pstate0 := pstate; pstate1 := pstate; pstate2 := pstate; apersistence_sync#(adr0, istore, istore0, ginval, gstore, gstore0, log1, m2, ns0; pstate, isbuf1; err1)⟩ ( abs-istore (avol0[pstate1.lnum, mapped(avol0[pstate1.lnum].data + subarray(buf1, 0, n))], lpt1 [buffered(pstate2.lnum).leb, mklp (lpt1[buffered(pstate2.lnum).leb].ref-size, LEB_SIZE, lpt1[buffered(pstate2.lnum).leb].flags, lpt1[buffered(pstate2.lnum).leb].gcheapidx) ], istore) ∧ abs-gstore (avol0[pstate1.lnum, mapped(avol0[pstate1.lnum].data + subarray(buf1, 0, n))], lpt1 [buffered(pstate2.lnum).leb, mklp (lpt1[buffered(pstate2.lnum).leb].ref-size, LEB_SIZE, lpt1[buffered(pstate2.lnum).leb].flags, lpt1[buffered(pstate2.lnum).leb].gcheapidx) ], gstore, ginval) ∧ ginval < # lpt1 [buffered(pstate2.lnum).leb, mklp (lpt1[buffered(pstate2.lnum).leb].ref-size, LEB_SIZE, lpt1[buffered(pstate2.lnum).leb].flags, lpt1[buffered(pstate2.lnum).leb].gcheapidx) ] ∧ (isbuf1 → synced(avol0[pstate1.lnum, mapped(avol0[pstate1.lnum].data + subarray(buf1, 0, n))])) ∧ pstate ≠ unbuffered ∧ (pstate = readonly ↔ isbuf2) ∧ (pstate ≠ readonly → pstate0.lnum = pstate.lnum) ∧ err0 = err1)), buf1 = mkbuf(0), lpf = LP_FREE, n = 0, pstate = readonly, pstate = unbuffered, dups(log1), is-aligned(# buf, EB_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 192:
# lpt1 = # avol0, # lpt0 = # avol0, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, avol0[pstate.lnum] = mapped(buf), lpt1[pstate.lnum] = mklp(m1, # buf, lpf, m4), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, buf1 ≠ mkbuf(0), lpf ≠ LP_FREE, n ≠ 0, pstate ≠ unbuffered, pstate ≠ readonly, ginval < # avol0, n < # buf1, pstate.lnum < # avol0, abs-gstore(avol0, lpt1, gstore, ginval), abs-istore(avol0, lpt1, istore), abs-padding(buf1), 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(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), is-aligned(# buf + n, EB_PAGE_SIZE), is-aligned(# buf, 2 * NODE_HEADER_SIZE), log-group-block(log1, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log1), # buf + # buf1 ≤ LEB_SIZE, # buf ≤ LEB_SIZE, istore0 ⊑ istore, ⌊err0⌋ , ¬ dups(log1), ¬ is-aligned(# buf, EB_PAGE_SIZE), pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? ∨ pstate.journal? ⊦ [awbuf_enter_readonly# (adr0, m2, log1, avol0[buffered(pstate.lnum).leb, mapped(avol0[buffered(pstate.lnum).leb].data + subarray(buf1, 0, n))], lpt0, ns0, buffered(pstate.lnum) ; ; isbuf2)] ( (lpt1[pstate.lnum].flags = LP_FREE → lpt1[pstate.lnum].ref-size = 0) ∧ freelist-cons(lpt1[pstate.lnum, mklp(lpt1[pstate.lnum].ref-size, LEB_SIZE, lpt1[pstate.lnum].flags, lpt1[pstate.lnum].gcheapidx)], freelist) ∧ bin-heap-inv(gch, lpt1[pstate.lnum, mklp(lpt1[pstate.lnum].ref-size, LEB_SIZE, lpt1[pstate.lnum].flags, lpt1[pstate.lnum].gcheapidx)]) ∧ keyset(gch) = gc-heap(lpt1[pstate.lnum, mklp(lpt1[pstate.lnum].ref-size, LEB_SIZE, lpt1[pstate.lnum].flags, lpt1[pstate.lnum].gcheapidx)], log1) ∧ log-group-block(log1, lpt1[pstate.lnum, mklp(lpt1[pstate.lnum].ref-size, LEB_SIZE, lpt1[pstate.lnum].flags, lpt1[pstate.lnum].gcheapidx)]) ∧ buf-ro-rw-mode (isbuf2, buffered(pstate.lnum), lpt1[pstate.lnum, mklp(lpt1[pstate.lnum].ref-size, LEB_SIZE, lpt1[pstate.lnum].flags, lpt1[pstate.lnum].gcheapidx)], avol0[pstate.lnum, mapped(avol0[pstate.lnum].data + subarray(buf1, 0, n))]) ∧ lpt-ram-flash (lpt1[pstate.lnum, mklp(lpt1[pstate.lnum].ref-size, LEB_SIZE, lpt1[pstate.lnum].flags, lpt1[pstate.lnum].gcheapidx)], lpt0, log1) ∧ awbuf-inv(avol0[pstate.lnum, mapped(avol0[pstate.lnum].data + subarray(buf1, 0, n))], buffered(pstate.lnum)) → ⟨isbuf1 := false; pstate0 := pstate; pstate1 := pstate; pstate2 := pstate; apersistence_sync#(adr0, istore, istore0, ginval, gstore, gstore0, log1, m2, ns0; pstate, isbuf1; err1)⟩ ( abs-istore (avol0[pstate1.lnum, mapped(avol0[pstate1.lnum].data + subarray(buf1, 0, n))], lpt1[pstate2.lnum, mklp(lpt1[pstate2.lnum].ref-size, LEB_SIZE, lpt1[pstate2.lnum].flags, lpt1[pstate2.lnum].gcheapidx)], istore) ∧ abs-gstore (avol0[pstate1.lnum, mapped(avol0[pstate1.lnum].data + subarray(buf1, 0, n))], lpt1[pstate2.lnum, mklp(lpt1[pstate2.lnum].ref-size, LEB_SIZE, lpt1[pstate2.lnum].flags, lpt1[pstate2.lnum].gcheapidx)], gstore, ginval) ∧ ginval < # lpt1 ∧ (isbuf1 → synced(avol0[pstate1.lnum, mapped(avol0[pstate1.lnum].data + subarray(buf1, 0, n))])) ∧ pstate ≠ unbuffered ∧ (pstate = readonly ↔ isbuf2) ∧ (pstate ≠ readonly → pstate0.lnum = pstate.lnum) ∧ err0 = err1))

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)% ⊦ mklp(n2, n3, lpf, m).size = n3; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)%⊦ lpt-leb-size(lpt) → (lpt-leb-size(lpt[n, lp]) ↔ # lpt ≤ n ∨ lp.size ≤ LEB_SIZE); (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).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)% ⊦ buffered(m).isbuf?; (s)% ⊦ buffered(m).leb = m; (s)