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Proof step 382 from proof refine-sync (previous step)

# lpt1 = # avol, # lpt0 = # avol, isbuf2 ↔ pstate = readonly, isbuf ↔ pstate = readonly, lpt1[bleb1.leb] = mklp(m1, m5, lpf, m4), adr = adr0, bleb = bleb1, err = ESUCCESS, keyset(gch) = gc-heap(lpt1, log1), log = log1, lpt = lpt0, m0 = lpt1[bleb1.leb].size, ns = ns0, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, bleb1.isbuf?, bleb1.leb < # lpt1, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, bleb1), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(isbuf2, bleb1, lpt1, avol), buf-ro-rw-mode(pstate = readonly, bleb1, lpt1, avol), bufs-log-only(bleb1, log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), is-aligned(m0, EB_PAGE_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), istore0 ⊑ istore, bleb1.isbuf? ∧ pstate ≠ readonly → bleb1.leb < # avol ∧ # avol[bleb1.leb].data ≤ LEB_SIZE ∧ avol[bleb1.leb].mapped? ∧ m5 = # avol[bleb1.leb].data ∧ lpf ≠ LP_FREE ∧ is-aligned(# avol[bleb1.leb].data, 2 * NODE_HEADER_SIZE), pstate = unbuffered → isbuf1, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb1 = buffered(pstate.lnum), pstate = unbuffered → bleb1 = nobuffer, isbuf1 → synced(avol) ⊦ ⟨apersistence_sync#(adr0, istore, istore0, ginval, gstore, gstore0, log1, m, ns0; pstate, isbuf1; err0)⟩ ( 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 = err0), pstate = readonly, dups(log1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 383:
# lpt1 = # avol, # lpt0 = # avol, lpt1[pstate.lnum] = mklp(m1, # buf, lpf, m4), avol[pstate.lnum] = mapped(buf), keyset(gch) = gc-heap(lpt1, log1), n = pstate.lnum, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, lpf ≠ LP_FREE, pstate ≠ readonly, pstate ≠ unbuffered, ginval < # avol, pstate.lnum < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), 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(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), 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), synced(avol), # buf ≤ LEB_SIZE, istore0 ⊑ istore, ¬ dups(log1), pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore ⊦ ⟨apersistence_sync#(adr0, istore, istore0, ginval, gstore, gstore0, log1, m, ns0; pstate, isbuf1; err0)⟩ (pstate ≠ unbuffered ∧ pstate ≠ readonly ∧ n = pstate.lnum ∧ ESUCCESS = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ n < # avol ∧ synced(avol) ∧ avol[n] = mapped(buf) → is-aligned(# buf, EB_PAGE_SIZE); (s)%n < # avol ⊦ awbuf-inv(avol, buffered(n)) ∧ avol[n] = mapped(buf) → (synced(avol) ↔ is-aligned(# buf, EB_PAGE_SIZE)); (ss)% ⊦ mapped(buf).data = buf; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv% ⊦ nobuffer ≠ buffered(m); (s)% ⊦ buffered(m) = buffered(m0) ↔ m = m0; (s)% ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf)); (as)% ⊦ buffered(m).isbuf?; (s)% ⊦ mklp(n2, n3, lpf, m).size = n3; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ buffered(m).leb = m; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ bleb.isbuf? ↔ (∃ n. bleb = buffered(n)); (as)