| m6 + # lpt = # avol, avol[m2] = mapped(buf3), avol[m3] = mapped(buf2), avol[0] = mapped(buf1), avol[m6 + m] = mapped(buf0), sb = mksb(adr, m1, m2, m3, m4, m5, m6), m < # lpt, disk-layout(sb, # lpt), ebm-vol-inv(avol), is-aligned(n, EB_PAGE_SIZE), is-aligned(m0, EB_PAGE_SIZE), is-encoded(sb, 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)), n0 + n ≤ # buf, m0 + n ≤ LEB_SIZE, # buf0 ≤ m0, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟪persistence_io_write#(m, m0, n0, n, buf, sb; avol; err)⟫ ( (∃ lpt0, log, orphans. disk-layout(sb, # lpt0) ∧ m6 + # lpt0 = # avol ∧ avol[0].mapped? ∧ is-encoded(sb, avol[0].data) ∧ avol[m3].mapped? ∧ is-encoded-pad(orphans, m4, avol[m3].data) ∧ avol[m2].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m2].data = logoff) ∧ is-encoded(log, avol[m2].data) ∧ mapped-full?(avol, m5, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, m5, lptlebs(# lpt0, LEB_SIZE)))) ∧ ebm-vol-inv(avol)) |
m6 + # lpt = # avol, avol[m6 + m] = mapped(buf0), avol[0] = mapped(buf1), avol[m3] = mapped(buf2), avol[m2] = mapped(buf3), m < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(avol), is-aligned(m0, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), 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)), # buf0 ≤ m0, m0 + n ≤ LEB_SIZE, n0 + n ≤ # buf, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟪persistence_io_write#(m, m0, n0, n, buf, mksb(adr, m1, m2, m3, m4, m5, m6); avol; err)⟫ ( (∃ lpt0, log, orphans. disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt0) ∧ m6 + # lpt0 = # avol ∧ avol[0].mapped? ∧ is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), avol[0].data) ∧ avol[m3].mapped? ∧ is-encoded-pad(orphans, m4, avol[m3].data) ∧ avol[m2].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m2].data = logoff) ∧ is-encoded(log, avol[m2].data) ∧ mapped-full?(avol, m5, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, m5, lptlebs(# lpt0, LEB_SIZE)))) ∧ ebm-vol-inv(avol))