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Proof step 256 from proof refine-sync (previous step)

# lpt0 = # avol0, # lpt1 = # avol0, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, avol0[pstate.lnum] = mapped(buf), lpt1[pstate.lnum] = mklp(m, # buf, LP_INDEX_NODES, m4), istore2[n0] = indexblock(indx, lax, m0), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, n < # buf1, ginval < # avol0, pstate.lnum < # avol0, abs-gstore(avol0, lpt1, gstore2, ginval), abs-istore(avol0, lpt1, istore2), abs-padding(buf1), awbuf-inv(avol0[pstate.lnum, mapped(buf + subarray(buf1, 0, n))], 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(# buf, 2 * NODE_HEADER_SIZE), 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[pstate.lnum, mklp(m, LEB_SIZE, LP_INDEX_NODES, m4)], lpt0, log1), # buf ≤ LEB_SIZE, # buf + # buf1 ≤ LEB_SIZE, istore1 ⊑ istore2, ⌊err1⌋ , pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? → pstate.lnum ∈ istore2, pstate.index? ∨ pstate.journal? ⊦ buf1 = mkbuf(0), n = 0, pstate = unbuffered, pstate = readonly, dups(log1), is-aligned(# buf, EB_PAGE_SIZE), (n0 < # avol0 ∧ lpt1[pstate.lnum, mklp(m, LEB_SIZE, LP_INDEX_NODES, m4)][n0].flags = LP_INDEX_NODES ↔ n0 ∈ istore2) ∧ ( n0 ∈ istore2 → abs-leb (avol0[pstate.lnum, mapped(buf + subarray(buf1, 0, n))][n0], indexblock(indx, lax, lpt1[pstate.lnum, mklp(m, LEB_SIZE, LP_INDEX_NODES, m4)][n0].ref-size), lpt1[pstate.lnum, mklp(m, LEB_SIZE, LP_INDEX_NODES, m4)][n0]) ∧ lpt1[pstate.lnum, mklp(m, LEB_SIZE, LP_INDEX_NODES, m4)][n0].ref-size = m0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 257:
# lpt1 = # avol0, # lpt0 = # avol0, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, istore2[n0] = indexblock(indx, lax, m0), lpt1[pstate.lnum] = mklp(m, # buf, LP_INDEX_NODES, m4), avol0[pstate.lnum] = mapped(buf), lpt1[pstate.lnum, mklp(m, LEB_SIZE, LP_INDEX_NODES, m4)][n0] = mklp(m1, m2, lpf, m3), 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, n < # buf1, abs-gstore(avol0, lpt1, gstore2, ginval), abs-istore(avol0, lpt1, istore2), abs-padding(buf1), awbuf-inv(avol0, buffered(pstate.lnum)), awbuf-inv(avol0[pstate.lnum, mapped(buf + subarray(buf1, 0, n))], 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), is-aligned(# buf + n, EB_PAGE_SIZE), 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[pstate.lnum, mklp(m, LEB_SIZE, LP_INDEX_NODES, m4)], lpt0, log1), lpt-ram-flash(lpt1, lpt0, log1), # buf + # buf1 ≤ LEB_SIZE, # buf ≤ LEB_SIZE, istore1 ⊑ istore2, ⌊err1⌋ , pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? ∨ pstate.journal? ⊦ buf1 = mkbuf(0), n = 0, pstate = readonly, pstate = unbuffered, dups(log1), is-aligned(# buf, EB_PAGE_SIZE), (n0 < # avol0 ∧ lpf = LP_INDEX_NODES ↔ n0 ∈ istore2) ∧ ( n0 ∈ istore2 → abs-leb (avol0[pstate.lnum, mapped(buf + subarray(buf1, 0, n))][n0], indexblock(indx, lax, m1), lpt1[pstate.lnum, mklp(m, LEB_SIZE, LP_INDEX_NODES, m4)][n0]) ∧ m1 = m0)

Rule argument

spec: lprops name: elim seq: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1) subst: [lp, m, m0, lpf, m1] → [lpt1[pstate.lnum, mklp(m, LEB_SIZE, LP_INDEX_NODES, m4)][n0], m1, m2, lpf, m3]

Additional information

Used simplifier rules: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lpt1[pstate.lnum, mklp(m, LEB_SIZE, LP_INDEX_NODES, m4)][n0], m1, m2, lpf, m3