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Proof step 189 from proof refine-add-ind (previous step)

# lpt1 = # avol, # buf1 = 2 * NODE_HEADER_SIZE + ind.alignedsize, # lpt0 = # avol, n0 < # avol ∧ lpf0 = LP_INDEX_NODES ↔ n0 ∈ istore, lpt1[n0] = mklp(m6, m7, lpf0, m8), lpt1[m1, mklp(m2, LEB_SIZE, LP_INDEX_NODES, m5)][n0] = mklp(m0, m3, lpf, m4), istore[m1] = indexblock(indx, lax, m2), lpt1[m1] = mklp(m2, # buf, LP_INDEX_NODES, m5), avol[m1] = mapped(buf), istore[n0] = indexblock(indx0, lax0, m), keyset(gch) = gc-heap(lpt1, log1), n0 = m1, remove-refsize0(istore0) = istore0, remove-refsize0(gstore1) = gstore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, ginval < # avol, n < # buf1, m1 < # avol, abs-gstore(avol, lpt1, gstore2, ginval), abs-node(buf1, ind), awbuf-inv(avol, buffered(m1)), awbuf-inv(avol[m1, mapped(buf + subarray(buf1, 0, n))], buffered(m1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(m1), lpt1, avol), bufs-log-only(buffered(m1), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore1), freelist-cons(lpt1, freelist), inv(indexblock(indx, lax, m2)), inv(istore0), inv(istore), inv(gstore1), inv(gstore2 \ ginval), is-aligned(# buf + n, 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[m1, mklp(m2, LEB_SIZE, LP_INDEX_NODES, m5)], lpt0, log1), lpt-ram-flash(lpt1, lpt0, log1), m1 ∈ istore, # buf + # buf1 ≤ LEB_SIZE, istore0 ⊑ istore, ⌊err1⌋ , n0 ∈ istore → abs-leb(avol[n0], indexblock(indx0, lax0, m), mklp(m, m7, lpf0, m8)) ∧ m6 = m, isbuf → synced(avol) ⊦ buf1 = mkbuf(0), n = 0, dups(log1), (n0 < # avol ∧ lpf = LP_INDEX_NODES ↔ n0 ∈ istore) ∧ (n0 ∈ istore → abs-leb(avol[m1, mapped(buf + subarray(buf1, 0, n))][n0], indexblock(indx0, lax0, m), mklp(m, m3, lpf, m4)) ∧ m0 = m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 190:
# lpt0 = # avol, # buf1 = 2 * NODE_HEADER_SIZE + ind.alignedsize, # lpt1 = # avol, avol[m1] = mapped(buf), istore[m1] = indexblock(indx0, lax0, m0), lpt1[m1] = mklp(m0, # buf, LP_INDEX_NODES, m4), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, m1 < # avol, n < # buf1, ginval < # avol, abs-gstore(avol, lpt1, gstore2, ginval), abs-leb(mapped(buf), indexblock(indx0, lax0, m0), mklp(m0, # buf, LP_INDEX_NODES, m4)), abs-node(buf1, ind), awbuf-inv(avol[m1, mapped(buf + subarray(buf1, 0, n))], buffered(m1)), awbuf-inv(avol, buffered(m1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(m1), lpt1, avol), bufs-log-only(buffered(m1), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore1), freelist-cons(lpt1, freelist), inv(gstore2 \ ginval), inv(gstore1), inv(istore), inv(istore0), inv(indexblock(indx0, lax0, m0)), is-aligned(# buf + n, EB_PAGE_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), lpt-ram-flash(lpt1[m1, mklp(m0, LEB_SIZE, LP_INDEX_NODES, m4)], lpt0, log1), m1 ∈ istore, # buf + # buf1 ≤ LEB_SIZE, istore0 ⊑ istore, ⌊err1⌋ , isbuf → synced(avol) ⊦ buf1 = mkbuf(0), n = 0, abs-leb(mapped(buf + subarray(buf1, 0, n)), indexblock(indx0, lax0, m0), mklp(m0, LEB_SIZE, LP_INDEX_NODES, m4)), dups(log1)

Rule argument

Additional information

Used simplifier rules: ⊦ indexblock(indx, lax, m) = indexblock(indx0, lax0, m0) ↔ indx = indx0 ∧ lax = lax0 ∧ m = m0; (ws)%fwd-inv-iblock: ⊦ inv(istore) ∧ n ∈ istore ∧ istore[n] = iblock → inv(iblock); (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)