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Proof step 98 from proof inv-commit (previous step)

# lebs(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE)) = lptsize(# lpt, LEB_SIZE), # lpt0 = # lpt, # avol = # avol0, (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt = # avol0, avol0[1] = mapped(buf1), avol0[3] = mapped(buf0), avol0[0] = mapped(buf2), sb0 = mksb(adr0, m2, 1, 3, m6, 5, 5 + 2 * lptlebs(# lpt, LEB_SIZE)), 2 < # avol0, 4 < # avol0, ebm-vol-inv(avol), ebm-vol-inv(avol0[2, mapped(mkbuf(0))][4, mapped(buf)]), ebm-vol-inv(avol0), ebm-vol-inv(avol0[2, mapped(mkbuf(0))]), ebm-vol-inv(avol2), is-encoded(mksb(adr0, m2, 1, 3, m6, 5, 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf2), is-encoded(lpt0, lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf1), is-encoded(lpt, lebs(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE))), is-encoded-pad(orphans, # orphans, buf), is-encoded-pad(orphans0, m6, buf0), mapped-full?(avol0, 5, lptlebs(# lpt, LEB_SIZE)), mapped-full?(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE)), range=(avol, 5 + 2 * lptlebs(# lpt, LEB_SIZE), avol0, 5 + 2 * lptlebs(# lpt, LEB_SIZE), # lpt), range=(avol, 0, avol0[2, mapped(mkbuf(0))][4, mapped(buf)], 0, 5 + lptlebs(# lpt, LEB_SIZE)), 5 + 2 * lptlebs(# lpt, LEB_SIZE) ≤ # avol0, 2 * lptlebs(# lpt, LEB_SIZE) + 5 ≤ # avol0, err = ESUCCESS → id○(avol2, avol, 0) ∧ is-encoded(mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf3) ∧ avol2[0] = mapped(buf3), logoff ≠ LEB_SIZE → # buf1 = logoff, err ≠ ESUCCESS → avol2 = avol, err = ESUCCESS ∨ ⌊err⌋ ⊦ err = ESUCCESS, (∃ lpt1, log, orphans. disk-layout(sb0, # lpt1) ∧ sb0.main + # lpt1 = # avol2 ∧ avol2[0].mapped? ∧ is-encoded(sb0, avol2[0].data) ∧ avol2[sb0.orph].mapped? ∧ is-encoded-pad(orphans, sb0.orphsize, avol2[sb0.orph].data) ∧ avol2[sb0.log].mapped? ∧ (logoff ≠ LEB_SIZE → # avol2[sb0.log].data = logoff) ∧ is-encoded(log, avol2[sb0.log].data) ∧ mapped-full?(avol2, sb0.lpt, lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol2, sb0.lpt, lptlebs(# lpt1, LEB_SIZE)))) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → sb0.indexaddr = adr ∧ sb0.maxino = m3 ∧ avol2[sb0.log].data = mkbuf(0) ∧ is-encoded(lpt, lebs(avol2, sb0.lpt, lptlebs(# avol2 - sb0.main, LEB_SIZE))) ∧ is-encoded-pad(orphans, sb0.orphsize, avol2[sb0.orph].data)) ∧ ( err ≠ ESUCCESS → sb0 = mksb(adr0, m2, 1, 3, m6, 5, sb0.main) ∧ avol2[1] = avol0[1] ∧ avol2[3] = avol0[3] ∧ lebs(avol2, 5, lptlebs(# avol2 - sb0.main, LEB_SIZE)) = lebs(avol0, 5, lptlebs(# avol2 - sb0.main, LEB_SIZE))) ∧ sb0.main = 5 + 2 * lptlebs(# lpt, LEB_SIZE) ∧ # avol2 = # avol0 ∧ subarray(avol2, sb0.main, # avol2 - sb0.main) = subarray(avol0, sb0.main, # avol2 - sb0.main)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 99:
# 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), 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, ⌊err⌋ , logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ (∃ lpt1. 2 * lptlebs(# lpt, LEB_SIZE) = 2 * lptlebs(# lpt1, LEB_SIZE) ∧ (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt1 = # avol0 ∧ mapped-full?(avol, 5, lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol, 5, lptlebs(# lpt1, LEB_SIZE)))) ∧ lebs(avol, 5, lptlebs(# avol0 - 5 + 2 * lptlebs(# lpt, LEB_SIZE), LEB_SIZE)) = lebs(avol0, 5, lptlebs(# avol0 - 5 + 2 * lptlebs(# lpt, LEB_SIZE), LEB_SIZE)) ∧ subarray(avol, 5 + 2 * lptlebs(# lpt, LEB_SIZE), # avol0 - 5 + 2 * lptlebs(# lpt, LEB_SIZE)) = subarray(avol0, 5 + 2 * lptlebs(# lpt, LEB_SIZE), # avol0 - 5 + 2 * lptlebs(# lpt, LEB_SIZE))

Rule argument

Additional information

Used simplifier rules: rangeeq-till-leb5-fwd: m < 5 ⊦ range=(avol1, 0, avol0, 0, 5 + n) → avol1[(* m)] = avol0[m];% ⊦ is-encoded(nx0, buf) → (is-encoded(nx1, buf) ↔ nx0 = nx1); (s)%⊦ is-encoded-pad(ns0, n, buf) → (is-encoded-pad(ns1, n, buf) ↔ ns0 = ns1); (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf).mapped?; (s)%m ≠ n ⊦ avol[(* m), aleb][(* n)] = avol[n]; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).lpt = m3; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).log = m0; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).orphsize = m2; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).orph = m1; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).main = m4; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ SB_LPT = 5; (s)% ⊦ SB_ORPH = 3; (s)%⊦ disk-layout(mksb(adr0, m1, 1, m3, m4, m5, m6), # lpt) ↔ m3 = SB_ORPH ∧ m5 = SB_LPT ∧ m6 = SB_LPT + 2 * lptlebs(# lpt, LEB_SIZE); (s)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)