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Proof step 61 from proof prepost-read-orphans (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 62:
⊦ ebm-vol-inv(avol) ↔ (∀ n. n < # avol ∧ avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE))
Proof step 63:
m4 + # lpt = # avol, avol[0] = mapped(buf2), avol[m1] = mapped(buf0 + buf), avol[m5] = mapped(buf1), LEB_SIZE < # orphans0 * ENCODED_NAT_SIZE, m1 < # avol, disk-layout(mksb(adr, m6, m5, m1, # orphans0, m3, m4), # lpt), is-aligned(# buf0 + # buf, EB_PAGE_SIZE), is-encoded(orphans0, buf0), 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)), logoff ≠ LEB_SIZE → # buf1 = logoff, ∀ n. n < # avol ∧ avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE) ⊦ # orphans0 = 0, orphans0 = ∅

Rule argument

spec: ebm-vol-inv name: ebm-vol-inv seq: ⊦ ebm-vol-inv(avol) ↔ (∀ n. n < # avol ∧ avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE)) subst: [avol] → [avol] flags: <all paths>

Additional information

Used terms: avol