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Proof step 64 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), 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, m1 < # avol ∧ avol[m1].mapped? → # avol[m1].data ≤ LEB_SIZE ∧ is-aligned(# avol[m1].data, EB_PAGE_SIZE) ⊦ # orphans0 = 0, orphans0 = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 65:
m4 + # lpt = # avol, avol[m5] = mapped(buf1), avol[m1] = mapped(buf0 + buf), avol[0] = mapped(buf2), m1 < # avol, LEB_SIZE < # orphans0 * ENCODED_NAT_SIZE, # buf0 + # buf < # orphans0 * ENCODED_NAT_SIZE, disk-layout(mksb(adr, m6, m5, m1, # orphans0, m3, m4), # lpt), 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)), # buf0 + # buf ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ # orphans0 = 0, orphans0 = ∅

Rule argument

Additional information

Used simplifier rules: fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf).mapped?; (s)