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Proof step 59 from proof inv-sync (previous step)

# lpt1 = # avol0, # lpt0 = # avol0, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, avol0[n] = mapped(buf0), lpt1[n] = mklp(m3, # buf0, lpf, m4), keyset(gch) = gc-heap(lpt1, log0), n < # avol0, abs-padding(buf1), awbuf-inv(avol0[n, mapped(buf0 + buf1)], buffered(n)), awbuf-inv(avol0, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol0), bufs-log-only(buffered(n), log0, lpt1), freelist-cons(lpt1, freelist), is-aligned(# buf0, 2 * NODE_HEADER_SIZE), log-group-block(log0, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log0), # buf0 ≤ LEB_SIZE, # buf0 + # buf1 ≤ LEB_SIZE ⊦ buf1 = mkbuf(0), gc-heap(lpt1, log0) = gc-heap(lpt1[n, mklp(m3, # buf0 + # buf1, lpf, m4)], log0), lpf = LP_FREE, is-aligned(# buf0, EB_PAGE_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: persistence-base name: gc-heap-write-other seq: lpf0 ≠ LP_GROUP_NODES, lpf1 ≠ LP_GROUP_NODES, n < # lpt ⊦ lpt[n] = mklp(m0, m1, lpf0, m2) → gc-heap(lpt[n, mklp(n0, n1, lpf1, n2)], nx) = gc-heap(lpt, nx) subst: [lpf0, m0, m1, m2, nx, n2, lpf1, n1, n0, n, lpt] → [lpf, m3, # buf0, m4, log0, m4, lpf, # buf0 + # buf1, m3, n, lpt1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ LP_FREE ≠ LP_GROUP_NODES; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n < # lpt ⊦ lpt[n] = mklp(m0, m1, LP_GROUP_NODES, m2) → gc-heap(lpt[n, mklp(m0, n1, LP_GROUP_NODES, n2)], nx) = gc-heap(lpt, nx); (s) Used terms: lpf, m3, # buf0, m4, log0, m4, lpf, # buf0 + # buf1, m3, n, lpt1