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Proof step 56 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), lpf = LP_FREE, is-aligned(# buf0, EB_PAGE_SIZE), gc-heap(lpt1, log0) = gc-heap(lpt1[n, mklp(m3, # buf0 + (EB_PAGE_SIZE - # buf0 % EB_PAGE_SIZE), lpf, m4)], log0) ∧ log-group-block(log0, lpt1[n, mklp(m3, # buf0 + (EB_PAGE_SIZE - # buf0 % EB_PAGE_SIZE), lpf, m4)]) ∧ EB_PAGE_SIZE + # buf0 ≤ LEB_SIZE + # buf0 % EB_PAGE_SIZE

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 57:
# lpt0 = # avol0, # lpt1 = # avol0, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, EB_PAGE_SIZE = n0 + # buf0 % EB_PAGE_SIZE, lpt1[n] = mklp(m3, # buf0, lpf, m4), avol0[n] = mapped(buf0), keyset(gch) = gc-heap(lpt1, log0), n < # avol0, abs-padding(buf1), awbuf-inv(avol0, buffered(n)), awbuf-inv(avol0[n, mapped(buf0 + buf1)], 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(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log0), # buf0 + # buf1 ≤ LEB_SIZE, # buf0 ≤ LEB_SIZE, # buf0 % EB_PAGE_SIZE ≤ EB_PAGE_SIZE ⊦ buf1 = mkbuf(0), lpf = LP_FREE, is-aligned(# buf0, EB_PAGE_SIZE), gc-heap(lpt1, log0) = gc-heap(lpt1[n, mklp(m3, # buf0 + n0, lpf, m4)], log0) ∧ log-group-block(log0, lpt1[n, mklp(m3, # buf0 + n0, lpf, m4)]) ∧ EB_PAGE_SIZE + # buf0 ≤ LEB_SIZE + # buf0 % EB_PAGE_SIZE

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [# buf0 % EB_PAGE_SIZE, EB_PAGE_SIZE, n0]

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # buf0 % EB_PAGE_SIZE, EB_PAGE_SIZE, n0