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Proof step 153 from proof refine-sync (previous step)

# lpt0 = # avol0, # lpt1 = # avol0, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, avol0[pstate.lnum] = mapped(buf0), lpt1[pstate.lnum] = mklp(m1, # buf0, LP_INDEX_NODES, m4), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, 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(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_INDEX_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, 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, abs-istore(avol0[pstate.lnum, mapped(buf0 + buf1)], lpt1[pstate.lnum, mklp(m1, # buf0 + # buf1, LP_INDEX_NODES, m4)], istore2), dups(log1), is-aligned(# buf0, EB_PAGE_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 154:
⊦ abs-istore(avol, lpt, istore) ↔ (∀ n. (n < # lpt ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore) ∧ (n ∈ istore → abs-leb(avol[n], istore[n], lpt[n]) ∧ lpt[n].ref-size = istore[n].ref-size))
Proof step 155:
# lpt1 = # avol0, # lpt0 = # avol0, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, lpt1[pstate.lnum] = mklp(m1, # buf0, LP_INDEX_NODES, m4), avol0[pstate.lnum] = mapped(buf0), 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-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(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), 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(m1, # buf0 + # buf1, LP_INDEX_NODES, m4)], lpt0, log1), # 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.lnum ∈ gstore2, pstate.index? ∨ pstate.journal? ⊦ buf1 = mkbuf(0), pstate = unbuffered, pstate = readonly, dups(log1), is-aligned(# buf0, EB_PAGE_SIZE), ∀ n. ( n < # lpt1[pstate.lnum, mklp(m1, # buf0 + # buf1, LP_INDEX_NODES, m4)] ∧ lpt1[pstate.lnum, mklp(m1, # buf0 + # buf1, LP_INDEX_NODES, m4)][n].flags = LP_INDEX_NODES ↔ n ∈ istore2) ∧ ( n ∈ istore2 → abs-leb (avol0[pstate.lnum, mapped(buf0 + buf1)][n], istore2[n], lpt1[pstate.lnum, mklp(m1, # buf0 + # buf1, LP_INDEX_NODES, m4)][n]) ∧ lpt1[pstate.lnum, mklp(m1, # buf0 + # buf1, LP_INDEX_NODES, m4)][n].ref-size = istore2[n].ref-size)

Rule argument

spec: persistence-base name: abs-istore-def seq: ⊦ abs-istore(avol, lpt, istore) ↔ (∀ n. ( n < # lpt ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore) ∧ ( n ∈ istore → abs-leb(avol[n], istore[n], lpt[n]) ∧ lpt[n].ref-size = istore[n].ref-size)) subst: [istore, lpt, avol] → [istore2, lpt1 [pstate.lnum, mklp(m1, # buf0 + # buf1, LP_INDEX_NODES, m4) ], avol0[pstate.lnum, mapped(buf0 + buf1)]] flags: <all paths>

Additional information

Used terms: istore2, lpt1[pstate.lnum, mklp(m1, # buf0 + # buf1, LP_INDEX_NODES, m4)], avol0[pstate.lnum, mapped(buf0 + buf1)]