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Proof step 25 from proof refine-add-log-leb (previous step)

# avol0 = # avol2, # avol2 = # lpt0 + m5, avol2[m6] = mapped(buf4), avol2[m1] = mapped(buf3), avol2[0] = mapped(buf2), avol0[0] = mapped(buf), avol0[m1] = mapped(buf0), avol0[m6] = mapped(buf1), subarray(avol2, m5, # lpt0) = subarray(avol0, m5, # lpt0), disk-layout(mksb(adr, m, m6, m1, m3, m4, m5), # lpt0), ebm-vol-inv(avol2), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m5, # lpt0)), is-encoded(mksb(adr, m, m6, m1, m3, m4, m5), buf2), is-encoded(plog, buf1), is-encoded(lpt0, lebs(avol0, m4, lptlebs(# lpt0, LEB_SIZE))), is-encoded(mksb(adr, m, m6, m1, m3, m4, m5), buf), is-encoded(lpt0, lebs(avol2, m4, lptlebs(# lpt0, LEB_SIZE))), is-encoded(plog, buf4), is-encoded-pad(orphans, m3, buf3), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol0, m4, lptlebs(# lpt0, LEB_SIZE)), mapped-full?(avol2, m4, lptlebs(# lpt0, LEB_SIZE)), m5 ≤ # avol2, ⌊err1⌋ , logoff ≠ LEB_SIZE → # buf1 = logoff, logoff0 ≠ LEB_SIZE → # buf4 = logoff0 ⊦ subarray(avol0, m5, # lpt0) = subarray(avol2, m5, # avol2 - m5) ∧ is-encoded(lpt0, lebs(avol2, m4, lptlebs(# avol2 - m5, LEB_SIZE)))

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# avol2, m5, n]

Additional information

Used simplifier rules: ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m + n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # avol2, m5, n