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Proof step 22 from proof inv-read (previous step)

m6 + # lpt = # avol, avol[0] = mapped(buf1), avol[m3] = mapped(buf2), avol[m2] = mapped(buf3), avol[m6 + m8] = mapped(buf4), m8 < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(avol), is-encoded(log, buf3), is-encoded(lpt, lebs(avol, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf1), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol, m5, lptlebs(# lpt, LEB_SIZE)), n2 + n1 ≤ # buf, m7 + n1 ≤ LEB_SIZE, ⌊err0⌋ , logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ∃ buf1. # buf1 = # buf ∧ range=(buf, 0, buf1, 0, n2) ∧ range=(buf, n2 + n1, buf1, n2 + n1, # buf - n2 + n1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
# buf = n0 + n2 + n1, m6 + # lpt = # avol, avol[m6 + m8] = mapped(buf4), avol[m2] = mapped(buf3), avol[m3] = mapped(buf2), avol[0] = mapped(buf1), m8 < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(avol), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf1), is-encoded(lpt, lebs(avol, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf3), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol, m5, lptlebs(# lpt, LEB_SIZE)), m7 + n1 ≤ LEB_SIZE, n2 + n1 ≤ # buf, ⌊err0⌋ , logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ∃ buf1. # buf1 = # buf ∧ range=(buf, 0, buf1, 0, n2) ∧ range=(buf, n2 + n1, buf1, n2 + n1, n0)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# buf, n2 + n1, n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # buf, n2 + n1, n