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Proof step 107 from proof refine-sync (previous step)

# lpt1 = # avol0, # lpt0 = # avol0, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, EB_PAGE_SIZE = n0 + # buf0 % EB_PAGE_SIZE, avol0[pstate.lnum] = mapped(buf0), lpt1[pstate.lnum] = mklp(m1, # buf0, lpf, m4), avol = avol0[pstate.lnum, mapped(buf0 + buf1)], bleb1 = buffered(pstate.lnum), gc-heap(lpt1, log1) = gc-heap(lpt1[pstate.lnum, mklp(m1, # buf0 + n0, lpf, m4)], log1), ¬ isbuf, keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, pstate.lnum < # avol0, ginval < # avol0, abs-gstore(avol0, lpt1, gstore, ginval), abs-istore(avol0, lpt1, istore), abs-padding(buf1), awbuf-inv(avol0, buffered(pstate.lnum)), awbuf-inv(avol0[pstate.lnum, mapped(buf0 + buf1)], 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(# buf0, 2 * NODE_HEADER_SIZE), log-group-block(log1, lpt1), log-group-block(log1, lpt1[pstate.lnum, mklp(m1, # buf0 + n0, lpf, m4)]), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log1), lpt-ram-flash(lpt1[pstate.lnum, mklp(m1, # buf0 + n0, lpf, m4)], lpt0, log1), # buf0 + # buf1 ≤ LEB_SIZE, # buf0 ≤ LEB_SIZE, EB_PAGE_SIZE + # buf0 ≤ LEB_SIZE + # buf0 % EB_PAGE_SIZE, # buf0 % EB_PAGE_SIZE ≤ EB_PAGE_SIZE, istore0 ⊑ istore, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, 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 + n0, 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 + n0, 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), buf1 = mkbuf(0), lpf = LP_FREE, pstate = readonly, pstate = unbuffered, dups(log1), is-aligned(# buf0, EB_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 108:
# lpt1 = # avol0, # lpt0 = # avol0, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, avol0[pstate.lnum] = mapped(buf0), lpt1[pstate.lnum] = mklp(m1, # buf0, lpf, m4), avol = avol0[pstate.lnum, mapped(buf0 + buf1)], bleb1 = buffered(pstate.lnum), gc-heap(lpt1, log1) = gc-heap(lpt1[pstate.lnum, mklp(m1, # buf0 + # buf1, lpf, m4)], log1), ¬ isbuf, 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, pstate ≠ readonly, pstate ≠ unbuffered, pstate.lnum < # avol0, ginval < # avol0, abs-gstore(avol0, lpt1, gstore, ginval), abs-istore(avol0, lpt1, istore), abs-padding(buf1), awbuf-inv(avol0, buffered(pstate.lnum)), awbuf-inv(avol0[pstate.lnum, mapped(buf0 + buf1)], 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(# buf0, 2 * NODE_HEADER_SIZE), log-group-block(log1, lpt1), log-group-block(log1, lpt1[pstate.lnum, mklp(m1, # buf0 + # buf1, lpf, m4)]), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log1), lpt-ram-flash(lpt1[pstate.lnum, mklp(m1, # buf0 + # buf1, lpf, m4)], lpt0, log1), # buf0 + # buf1 ≤ LEB_SIZE, # buf0 ≤ LEB_SIZE, EB_PAGE_SIZE + # buf0 ≤ LEB_SIZE + # buf0 % EB_PAGE_SIZE, istore0 ⊑ istore, ¬ dups(log1), ¬ is-aligned(# buf0, EB_PAGE_SIZE), pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, 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 + # buf1, 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 + # buf1, 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: eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)