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Proof step 37 from proof prepost-read-orphans (previous step)

m4 + # lpt = # avol, LEB_SIZE = n0 + # buf3 + # buf0, avol[0] = mapped(buf2), avol[m1] = mapped(buf3 + buf0), avol[m5] = mapped(buf1), m1 < # avol, # buf3 < # orphans0 * ENCODED_NAT_SIZE, # buf3 < LEB_SIZE, disk-layout(mksb(adr, m6, m5, m1, # orphans0, m3, m4), # lpt), ebm-vol-inv(avol), is-aligned(# buf3 + # buf0, EB_PAGE_SIZE), is-encoded(orphans0, buf3), is-encoded(log, buf1), is-encoded(lpt, lebs(avol, m3, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m6, m5, m1, # orphans0, m3, m4), buf2), mapped-full?(avol, m3, lptlebs(# lpt, LEB_SIZE)), # buf3 + # buf0 ≤ LEB_SIZE, # orphans0 * ENCODED_NAT_SIZE ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ # orphans0 = 0, n0 + # buf0 = 0, orphans0 = ∅, is-encoded(orphans0, subarray(buf3 + buf0 + mkempbuf(n0), 0, # orphans0 * ENCODED_NAT_SIZE))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: encoding-orphans name: is-encoded-size seq: ⊦ is-encoded(ns, buf) → # buf = # ns * ENCODED_NAT_SIZE subst: [ns, buf] → [orphans0, buf3] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ m0 ≠ 0 → (m0 * m < m0 * n ↔ m < n); (s)% ⊦ ¬ n < n; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: orphans0, buf3