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Proof step 286 from proof refine-sync (previous step)

# lpt0 = # avol, # lpt1 = # avol, isbuf2 ↔ true, isbuf ↔ false, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, avol[pstate.lnum] = mapped(buf), lpt1[pstate.lnum] = mklp(m1, # buf, lpf, m4), bleb1 = buffered(pstate.lnum), buf0 = buf1, err = err0, keyset(gch) = gc-heap(lpt1, log1), m = buffered(pstate.lnum).leb, m0 = lpt1[buffered(pstate.lnum).leb].size, n0 = # buf1, 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, ginval < # avol, pstate.lnum < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), abs-padding(buf1), awbuf-inv(avol, buffered(pstate.lnum)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt1, avol), 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), 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, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, ∀ n. (n ≠ 0 → n < n0 → avol[m].mapped? ∧ m < # avol) ∧ ¬(n ≠ 0 ∧ n < n0 ∧ is-aligned(# avol[m].data + n, EB_PAGE_SIZE)), ⌊err0⌋ ∨ err0 = ESUCCESS, pstate.index? ∨ pstate.journal? ⊦ [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#(adr0, m2, log1, avol, lpt0, ns0, bleb1; ; isbuf2)] ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log1) ∧ bufs-log-only(bleb1, log1, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log1, lpt1) ∧ buf-ro-rw-mode(isbuf2, bleb1, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log1) ∧ awbuf-inv(avol, bleb1) ∧ # lpt0 = # avol → ⟨isbuf1 := false; apersistence_sync#(adr0, istore, istore0, ginval, gstore, gstore0, log1, m2, ns0; pstate, isbuf1; err1)⟩ ( abs-istore(avol, lpt1, istore) ∧ abs-gstore(avol, lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (isbuf1 → synced(avol)) ∧ (pstate = unbuffered → bleb1 = nobuffer) ∧ (pstate = readonly ↔ isbuf2) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb1 = buffered(pstate.lnum)) ∧ err = err1)), buf1 = mkbuf(0), err = ESUCCESS, lpf = LP_FREE, 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 287:
# lpt0 = # avol, # lpt1 = # avol, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, avol[pstate.lnum] = mapped(buf), lpt1[pstate.lnum] = mklp(m1, # buf, lpf, m4), 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 < # avol, pstate.lnum < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), abs-padding(buf1), awbuf-inv(avol, buffered(pstate.lnum)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt1, avol), 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), 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⌋ , ¬ dups(log1), ¬ is-aligned(# buf, EB_PAGE_SIZE), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, ∀ n. n = 0 ∨ ¬ n < # buf1 ∨ ¬ is-aligned(# buf + n, EB_PAGE_SIZE), pstate.index? ∨ pstate.journal? ⊦ [debug#("persistence: flushing of LEB " + buffered(pstate.lnum).leb.toString + " failed"); 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); awbuf_enter_readonly#(adr0, m2, log1, avol, lpt0, ns0, buffered(pstate.lnum); ; isbuf2)] ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log1) ∧ bufs-log-only(buffered(pstate.lnum), log1, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log1, lpt1) ∧ buf-ro-rw-mode(isbuf2, buffered(pstate.lnum), lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log1) → ⟨isbuf1 := false; pstate0 := pstate; apersistence_sync#(adr0, istore, istore0, ginval, gstore, gstore0, log1, m2, ns0; pstate, isbuf1; err1)⟩ ( abs-istore(avol, lpt1, istore) ∧ abs-gstore(avol, lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (isbuf1 → synced(avol)) ∧ pstate ≠ unbuffered ∧ (pstate = readonly ↔ isbuf2) ∧ (pstate ≠ readonly → pstate0.lnum = pstate.lnum) ∧ err0 = err1))

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ buffered(m) = buffered(m0) ↔ m = m0; (s)% ⊦ nobuffer ≠ buffered(m); (s)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)% ⊦ buffered(m).isbuf?; (s)% ⊦ buffered(m).leb = m; (s)