| m8 + # lpt0 = # avol, avol[0] = mapped(buf), avol[m5] = mapped(buf0), avol[m1] = mapped(buf1), sb = mksb(adr0, m0, m1, m5, m6, m7, m8), disk-layout(sb, # lpt0), ebm-vol-inv(avol), is-encoded(log0, buf1), is-encoded(lpt0, lebs(avol, m7, lptlebs(# lpt0, LEB_SIZE))), is-encoded(sb, buf), is-encoded-pad(orphans0, m6, buf0), mapped-full?(avol, m7, lptlebs(# lpt0, LEB_SIZE)), avol ⊆ avol0, m ≠ LEB_SIZE → # buf1 = m ⊦ ⟪persistence_io_recover#(; adr, m2, orphans, log, lpt, sb0, logoff, m3, m4, avol0; err)⟫ ( ( err = ESUCCESS → (∃ lpt1, log1, orphans1. disk-layout(sb0, # lpt1) ∧ sb0.main + # lpt1 = # avol0 ∧ avol0[0].mapped? ∧ is-encoded(sb0, avol0[0].data) ∧ avol0[sb0.orph].mapped? ∧ is-encoded-pad(orphans1, sb0.orphsize, avol0[sb0.orph].data) ∧ avol0[sb0.log].mapped? ∧ (logoff ≠ LEB_SIZE → # avol0[sb0.log].data = logoff) ∧ is-encoded(log1, avol0[sb0.log].data) ∧ mapped-full?(avol0, sb0.lpt, lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol0, sb0.lpt, lptlebs(# lpt1, LEB_SIZE)))) ∧ m3 = EB_PAGE_SIZE ∧ m4 = LEB_SIZE ∧ ebm-vol-inv(avol0)) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → sb0 = sb ∧ # avol0 = # avol ∧ adr = adr0 ∧ m2 = m0 ∧ # lpt = # avol0 - m8 ∧ is-encoded(lpt, lebs(avol0, m7, lptlebs(# avol0 - m8, LEB_SIZE))) ∧ lebs(avol0, m7, lptlebs(# avol0 - m8, LEB_SIZE)) = lebs(avol, m7, lptlebs(# avol0 - m8, LEB_SIZE)) ∧ is-encoded(log, avol0[m1].data) ∧ is-encoded-pad(orphans, m6, avol0[m5].data) ∧ avol0[m5] = avol[m5] ∧ avol0[m1] = avol[m1])) |
m8 + # lpt0 = # avol, avol[m1] = mapped(buf1), avol[m5] = mapped(buf0), avol[0] = mapped(buf), disk-layout(mksb(adr0, m0, m1, m5, m6, m7, m8), # lpt0), ebm-vol-inv(avol), is-encoded(mksb(adr0, m0, m1, m5, m6, m7, m8), buf), is-encoded(lpt0, lebs(avol, m7, lptlebs(# lpt0, LEB_SIZE))), is-encoded(log0, buf1), is-encoded-pad(orphans0, m6, buf0), mapped-full?(avol, m7, lptlebs(# lpt0, LEB_SIZE)), avol ⊆ avol0, m ≠ LEB_SIZE → # buf1 = m ⊦ ⟪persistence_io_recover#(; adr, m2, orphans, log, lpt, sb0, logoff, m3, m4, avol0; err)⟫ ( ( err = ESUCCESS → (∃ lpt1, log1, orphans1. disk-layout(sb0, # lpt1) ∧ sb0.main + # lpt1 = # avol0 ∧ avol0[0].mapped? ∧ is-encoded(sb0, avol0[0].data) ∧ avol0[sb0.orph].mapped? ∧ is-encoded-pad(orphans1, sb0.orphsize, avol0[sb0.orph].data) ∧ avol0[sb0.log].mapped? ∧ (logoff ≠ LEB_SIZE → # avol0[sb0.log].data = logoff) ∧ is-encoded(log1, avol0[sb0.log].data) ∧ mapped-full?(avol0, sb0.lpt, lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol0, sb0.lpt, lptlebs(# lpt1, LEB_SIZE)))) ∧ m3 = EB_PAGE_SIZE ∧ m4 = LEB_SIZE ∧ ebm-vol-inv(avol0)) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → sb0 = mksb(adr0, m0, m1, m5, m6, m7, m8) ∧ # avol0 = # avol ∧ adr = adr0 ∧ m2 = m0 ∧ # lpt = # avol0 - m8 ∧ is-encoded(lpt, lebs(avol0, m7, lptlebs(# avol0 - m8, LEB_SIZE))) ∧ lebs(avol0, m7, lptlebs(# avol0 - m8, LEB_SIZE)) = lebs(avol, m7, lptlebs(# avol0 - m8, LEB_SIZE)) ∧ is-encoded(log, avol0[m1].data) ∧ is-encoded-pad(orphans, m6, avol0[m5].data) ∧ avol0[m5] = avol[m5] ∧ avol0[m1] = avol[m1]))