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Proof step 144 from proof refine-sync (previous step)

# lpt0 = # avol0, # lpt1 = # avol0, n < # avol0 ∧ lpf0 = LP_GROUP_NODES ↔ n ∈ gstore2, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, lpt1[pstate.lnum, mklp(m1, # buf0 + # buf1, LP_GROUP_NODES, m4)][n] = mklp(m0, m2, lpf, m3), gstore2[n] = groupblock(gndx, lax, m), avol0[pstate.lnum] = mapped(buf0), lpt1[pstate.lnum] = mklp(m1, # buf0, LP_GROUP_NODES, m4), lpt1[n] = mklp(m5, m6, lpf0, m7), keyset(gch) = gc-heap(lpt1, log1), n = pstate.lnum, remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, ginval < # avol0, pstate.lnum < # avol0, abs-istore(avol0, lpt1, istore2), abs-padding(buf1), awbuf-inv(avol0[pstate.lnum, mapped(buf0 + buf1)], buffered(pstate.lnum)), 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, istore1, gstore1), freelist-cons(lpt1, freelist), inv(gstore2 \ ginval), inv(gstore1), inv(istore2), inv(istore1), is-aligned(# buf0, 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[pstate.lnum, mklp(m1, # buf0 + # buf1, LP_GROUP_NODES, m4)], lpt0, log1), lpt-ram-flash(lpt1, lpt0, log1), EB_PAGE_SIZE + # buf0 ≤ LEB_SIZE + # buf0 % EB_PAGE_SIZE, # buf0 ≤ LEB_SIZE, # buf0 + # buf1 ≤ LEB_SIZE, istore1 ⊑ istore2, n ∈ gstore2 → m5 = m, n ∈ gstore2 ∧ ¬ n ∈ ginval → abs-leb(avol0[n], groupblock(gndx, lax, m), mklp(m5, m6, lpf0, m7)), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? → pstate.lnum ∈ istore2, pstate.index? ∨ pstate.journal? ⊦ buf1 = mkbuf(0), pstate = readonly, pstate = unbuffered, dups(log1), is-aligned(# buf0, EB_PAGE_SIZE), (n < # avol0 ∧ lpf = LP_GROUP_NODES ↔ n ∈ gstore2) ∧ (n ∈ gstore2 ∧ ¬ n ∈ ginval → abs-leb(avol0[pstate.lnum, mapped(buf0 + buf1)][n], groupblock(gndx, lax, m), mklp(m0, m2, lpf, m3))) ∧ (n ∈ gstore2 → m0 = m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 145:
# lpt1 = # avol0, # lpt0 = # avol0, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, lpt1[pstate.lnum] = mklp(m, # buf0, LP_GROUP_NODES, m7), avol0[pstate.lnum] = mapped(buf0), gstore2[pstate.lnum] = groupblock(gndx, lax, m), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, pstate.lnum < # avol0, ginval < # avol0, abs-istore(avol0, lpt1, istore2), abs-leb(mapped(buf0), groupblock(gndx, lax, m), mklp(m, # buf0, LP_GROUP_NODES, m7)), 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, istore1, gstore1), freelist-cons(lpt1, freelist), inv(istore1), inv(istore2), inv(gstore1), inv(gstore2 \ ginval), inv(groupblock(gndx, lax, m)), is-aligned(# buf0, 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), lpt-ram-flash(lpt1[pstate.lnum, mklp(m, # buf0 + # buf1, LP_GROUP_NODES, m7)], lpt0, log1), pstate.lnum ∈ gstore2, # buf0 + # buf1 ≤ LEB_SIZE, # buf0 ≤ LEB_SIZE, EB_PAGE_SIZE + # buf0 ≤ LEB_SIZE + # buf0 % EB_PAGE_SIZE, istore1 ⊑ istore2, pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last, pstate.index? ∨ pstate.journal? ⊦ buf1 = mkbuf(0), pstate = unbuffered, pstate = readonly, abs-leb(mapped(buf0 + buf1), groupblock(gndx, lax, m), mklp(m, # buf0 + # buf1, LP_GROUP_NODES, m7)), dups(log1), is-aligned(# buf0, EB_PAGE_SIZE), pstate.lnum ∈ ginval

Rule argument

Additional information

Used simplifier rules: fwd-inv-gblock-rem: ⊦ inv(gstore \ ginval) ∧ n ∈ gstore ∧ ¬ n ∈ ginval ∧ gstore[n] = gblock → inv(gblock); (forward) from specification apersistence-base% ⊦ m < # avol → avol[m, aleb][m] = aleb; (s)%⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws)%m < # lpt ⊦ lpt[m, lp][m] = lp; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)