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Proof step 13 from proof refine-get-volume-size (previous step)

# avol = # lpt0 + m4, avol[m0] = mapped(buf1), avol[m1] = mapped(buf0), avol[0] = mapped(buf), disk-layout(mksb(adr, m, m0, m1, m2, m3, m4), # lpt0), ebm-vol-inv(avol), ebm-vol-inv(subarray(avol, m4, # lpt0)), is-encoded(mksb(adr, m, m0, m1, m2, m3, m4), buf), is-encoded(lpt0, lebs(avol, m3, lptlebs(# lpt0, LEB_SIZE))), is-encoded(log, buf1), is-encoded-pad(orphans, m2, buf0), mapped-full?(avol, m3, lptlebs(# lpt0, LEB_SIZE)), m4 ≤ # avol, # avol ≥ m4, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟨apersistence_io_get_volume_size#(adr, m, log, subarray(avol, m4, # lpt0), lpt0, orphans; ; n0)⟩ (# avol - m4 = n0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
# avol = # lpt0 + m4, # avol = n1 + m4, avol[0] = mapped(buf), avol[m1] = mapped(buf0), avol[m0] = mapped(buf1), disk-layout(mksb(adr, m, m0, m1, m2, m3, m4), # lpt0), ebm-vol-inv(subarray(avol, m4, # lpt0)), ebm-vol-inv(avol), is-encoded(log, buf1), is-encoded(lpt0, lebs(avol, m3, lptlebs(# lpt0, LEB_SIZE))), is-encoded(mksb(adr, m, m0, m1, m2, m3, m4), buf), is-encoded-pad(orphans, m2, buf0), mapped-full?(avol, m3, lptlebs(# lpt0, LEB_SIZE)), m4 ≤ # avol, # avol ≥ m4, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟨apersistence_io_get_volume_size#(adr, m, log, subarray(avol, m4, # lpt0), lpt0, orphans; ; n0)⟩ (n1 = n0)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# avol, m4, n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # avol, m4, n