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Proof step 186 from proof refine-sync (previous step)

# lpt0 = # avol0, # lpt1 = # avol0, isbuf2 ↔ true, isbuf ↔ false, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, avol0[pstate.lnum] = mapped(buf), lpt1[pstate.lnum] = mklp(m1, # buf, lpf, m4), avol = avol0[m, mapped(avol0[m].data + subarray(buf0, 0, n))], 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?, avol0[m].mapped?, buffered(pstate.lnum).leb < # lpt1, m < # avol0, n < n0, ginval < # avol0, 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(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), is-aligned(# avol0[m].data + n, EB_PAGE_SIZE), 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), 0 + n ≤ # buf0, # buf ≤ LEB_SIZE, # buf + # buf1 ≤ LEB_SIZE, istore0 ⊑ istore, n ≠ 0 → n < n0 → avol0[m].mapped? ∧ m < # avol0, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, ⌊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, 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

Rule argument

Additional information

Used simplifier rules: ⊦ 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%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ buffered(m) = buffered(m0) ↔ m = m0; (s)% ⊦ nobuffer ≠ buffered(m); (s)% ⊦ # avol[n, aleb] = # avol; (s)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)% ⊦ buffered(m).isbuf?; (s)% ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf)); (as)% ⊦ buffered(m).leb = m; (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)