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Proof step 43 from proof prepost-read-orphans (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ is-encoded(ns, buf) → # buf = # ns * ENCODED_NAT_SIZE

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 terms: orphans0, buf3