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Proof step 8 from proof refine-get-volume-size (previous step)

# avol = # lpt0 + m4, avol[m0] = mapped(buf1), avol[m1] = mapped(buf0), avol[0] = mapped(buf), sb = mksb(adr, m, m0, m1, m2, m3, m4), 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, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪ebm_avol_get_volume_size#(avol; ; n); n := n - sb.main⟫ ⟨apersistence_io_get_volume_size#(adr, m, log, subarray(avol, m4, # lpt0), lpt0, orphans; ; n0)⟩ (n = n0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
# avol = # lpt0 + m4, avol[0] = mapped(buf), avol[m1] = mapped(buf0), avol[m0] = mapped(buf1), sb = mksb(adr, m, m0, m1, m2, m3, m4), sb = mksb(adr0, m5, m6, m7, m8, m9, m10), 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, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪ebm_avol_get_volume_size#(avol; ; n); n := n - m10⟫ ⟨apersistence_io_get_volume_size#(adr, m, log, subarray(avol, m4, # lpt0), lpt0, orphans; ; n0)⟩ (n = n0)

Rule argument

spec: superblock name: elim seq: ⊦ ( ( ( ( (adr = sb.indexaddr ∧ m = sb.maxino) ∧ m0 = sb.log) ∧ m1 = sb.orph) ∧ m2 = sb.orphsize) ∧ m3 = sb.lpt) ∧ m4 = sb.main ↔ sb = mksb(adr, m, m0, m1, m2, m3, m4) subst: [sb, adr, m, m0, m1, m2, m3] → [sb, adr0, m4, m5, m6, m7, m8]

Additional information

Used simplifier rules: ⊦ ( ( ( ((adr = sb.indexaddr ∧ m = sb.maxino) ∧ m0 = sb.log) ∧ m1 = sb.orph) ∧ m2 = sb.orphsize) ∧ m3 = sb.lpt) ∧ m4 = sb.main ↔ sb = mksb(adr, m, m0, m1, m2, m3, m4); (elim) Used terms: sb, adr0, m4, m5, m6, m7, m8