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Proof step 31 from proof prepost-read-orphans (previous step)

m4 + # lpt = # avol, LEB_SIZE = n0 + # buf, avol[0] = mapped(buf2), avol[m1] = mapped(buf), avol[m5] = mapped(buf1), m2 = # orphans0, m1 < # avol, disk-layout(mksb(adr, m6, m5, m1, m2, m3, m4), # lpt), ebm-vol-inv(avol), is-encoded(log, buf1), is-encoded(lpt, lebs(avol, m3, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m6, m5, m1, m2, m3, m4), buf2), mapped-full?(avol, m3, lptlebs(# lpt, LEB_SIZE)), # buf ≤ LEB_SIZE, m2 * ENCODED_NAT_SIZE ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf1 = logoff, ∃ buf0, buf1. is-aligned(# buf, EB_PAGE_SIZE) ∧ buf = buf0 + buf1 ∧ is-encoded(orphans0, buf0) ⊦ is-encoded(orphans0, subarray(buf + mkempbuf(n0), 0, # orphans0 * ENCODED_NAT_SIZE)) ∧ m2 = # orphans0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
m4 + # lpt = # avol, LEB_SIZE = n0 + # buf3 + # buf0, avol[m5] = mapped(buf1), avol[m1] = mapped(buf3 + buf0), avol[0] = mapped(buf2), 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 ⊦ is-encoded(orphans0, subarray((buf3 + buf0) + mkempbuf(n0), 0, # orphans0 * ENCODED_NAT_SIZE))

Rule argument

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)