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Proof step 84 from proof inv-commit (previous step)

# avol = # avol0, # lpt0 = # lpt, # lebs(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE)) = lptsize(# lpt, LEB_SIZE), (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt = # avol0, avol0[0] = mapped(buf2), avol0[3] = mapped(buf0), avol0[1] = mapped(buf1), avol1 = avol, 4 < # avol0, 2 < # avol0, ebm-vol-inv(avol0[2, mapped(mkbuf(0))]), ebm-vol-inv(avol0), ebm-vol-inv(avol0[2, mapped(mkbuf(0))][4, mapped(buf)]), ebm-vol-inv(avol), is-encoded(lpt, lebs(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf1), is-encoded(lpt0, lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr0, m2, 1, 3, m6, 5, 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf2), is-encoded-pad(orphans0, m6, buf0), is-encoded-pad(orphans, # orphans, buf), mapped-full?(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE)), mapped-full?(avol0, 5, lptlebs(# lpt, LEB_SIZE)), range=(avol, 0, avol0[2, mapped(mkbuf(0))][4, mapped(buf)], 0, 5 + lptlebs(# lpt, LEB_SIZE)), range=(avol, 5 + 2 * lptlebs(# lpt, LEB_SIZE), avol0, 5 + 2 * lptlebs(# lpt, LEB_SIZE), # lpt), 2 * lptlebs(# lpt, LEB_SIZE) + 5 ≤ # avol0, 5 + 2 * lptlebs(# lpt, LEB_SIZE) ≤ # avol0, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ [persistence_io_write_superblock# (mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)), EB_PAGE_SIZE, LEB_SIZE; avol; err0)] ( (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ ebm-vol-inv(avol) ∧ ( err0 = ESUCCESS → id○(avol, avol1, 0) ∧ (∃ buf. is-encoded(mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf) ∧ avol[0] = mapped(buf))) ∧ (err0 ≠ ESUCCESS → avol = avol1) → ⟪sb0 := mksb(adr0, m2, 1, 3, m6, 5, 5 + 2 * lptlebs(# lpt, LEB_SIZE)); if err0 = ESUCCESS then {sb0 := mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)); logoff := 0}⟫ ( (∃ lpt1, log, orphans. disk-layout(sb0, # lpt1) ∧ sb0.main + # lpt1 = # avol ∧ avol[0].mapped? ∧ is-encoded(sb0, avol[0].data) ∧ avol[sb0.orph].mapped? ∧ is-encoded-pad(orphans, sb0.orphsize, avol[sb0.orph].data) ∧ avol[sb0.log].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[sb0.log].data = logoff) ∧ is-encoded(log, avol[sb0.log].data) ∧ mapped-full?(avol, sb0.lpt, lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol, sb0.lpt, lptlebs(# lpt1, LEB_SIZE)))) ∧ (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ ( err0 = ESUCCESS → sb0.indexaddr = adr ∧ sb0.maxino = m3 ∧ avol[sb0.log].data = mkbuf(0) ∧ is-encoded(lpt, lebs(avol, sb0.lpt, lptlebs(# avol - sb0.main, LEB_SIZE))) ∧ is-encoded-pad(orphans, sb0.orphsize, avol[sb0.orph].data)) ∧ ( err0 ≠ ESUCCESS → sb0 = mksb(adr0, m2, 1, 3, m6, 5, sb0.main) ∧ avol[1] = avol0[1] ∧ avol[3] = avol0[3] ∧ lebs(avol, 5, lptlebs(# avol - sb0.main, LEB_SIZE)) = lebs(avol0, 5, lptlebs(# avol - sb0.main, LEB_SIZE))) ∧ sb0.main = 5 + 2 * lptlebs(# lpt, LEB_SIZE) ∧ # avol = # avol0 ∧ subarray(avol, sb0.main, # avol - sb0.main) = subarray(avol0, sb0.main, # avol - sb0.main)))

User applied rule skip call

And obtained the following new goals

Rule argument

pos: right 1

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