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Proof step 90 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), err = ESUCCESS, sb0 = mksb(adr0, m2, 1, 3, m6, 5, 5 + 2 * lptlebs(# lpt, LEB_SIZE)), 4 < # avol0, 2 < # avol0, ebm-vol-inv(avol2), 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 ≠ ESUCCESS → avol2 = avol, logoff ≠ LEB_SIZE → # buf1 = logoff, 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), err = ESUCCESS ∨ ⌊err⌋ ⊦ (∃ lpt1, log, orphans0. disk-layout(mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)), # lpt1) ∧ mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).main + # lpt1 = # avol2 ∧ avol2[0].mapped? ∧ is-encoded(mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)), avol2[0].data) ∧ avol2[mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).orph].mapped? ∧ is-encoded-pad (orphans0, mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).orphsize, avol2[mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).orph].data) ∧ avol2[mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).log].mapped? ∧ ( 0 ≠ LEB_SIZE → # avol2[mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).log].data = 0) ∧ is-encoded(log, avol2[mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).log].data) ∧ mapped-full? (avol2, mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).lpt, lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded (lpt1, lebs (avol2, mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).lpt, lptlebs(# lpt1, LEB_SIZE)))) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).indexaddr = adr ∧ mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).maxino = m3 ∧ avol2[mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).log].data = mkbuf(0) ∧ is-encoded (lpt, lebs (avol2, mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).lpt, lptlebs (# avol2 - mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).main, LEB_SIZE))) ∧ is-encoded-pad (orphans, mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).orphsize, avol2[mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).orph].data)) ∧ ( err ≠ ESUCCESS → mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)) = mksb (adr0, m2, 1, 3, m6, 5, mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).main) ∧ avol2[1] = avol0[1] ∧ avol2[3] = avol0[3] ∧ lebs (avol2, 5, lptlebs (# avol2 - mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).main, LEB_SIZE)) = lebs (avol0, 5, lptlebs (# avol2 - mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).main, LEB_SIZE))) ∧ mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).main = 5 + 2 * lptlebs(# lpt, LEB_SIZE) ∧ # avol2 = # avol0 ∧ subarray (avol2, mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).main, # avol2 - mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).main) = subarray (avol0, mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).main, # avol2 - mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)).main)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: id-circle-subarray-concrete-below: n0 < n, n + m + m0 ≤ # avol ⊦ id○(avol, avol0, (* n0)) → subarray(avol, (* n) + m, m0) = subarray(avol0, n + m, m0);%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf).mapped?; (s)%idexcept-size: ⊦ id○(avol, avol0, n) → # avol = # avol0; (forward) from specification array-copy[avolume]%⊦ is-encoded-pad(ns0, n, buf) → (is-encoded-pad(ns1, n, buf) ↔ ns0 = ns1); (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m ≤ m; (s)%0 ≠ m ⊦ (* m) * n ≤ m * n0 ↔ n ≤ n0; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).maxino = m; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).indexaddr = adr; (s)%n < m0 ⊦ id○(avol1, avol0, n) → (mapped-full?(avol1, m0, m1) ↔ mapped-full?(avol0, m0, m1)); (s)%n < n0 ⊦ (* n) ≠ m0 + (* n0); (s)% ⊦ 0 < m ↔ m ≠ 0; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).lpt = m3; (s)% ⊦ LEB_SIZE ≠ 0; (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)% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ SB_LPT = 5; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ SB_ORPH = 3; (s)%⊦ disk-layout(mksb(adr0, m1, 2, m3, m4, m5, m6), # lpt) ↔ m3 = SB_ORPH + 1 ∧ m5 = SB_LPT + lptlebs(# lpt, LEB_SIZE) ∧ m6 = SB_LPT + 2 * lptlebs(# lpt, LEB_SIZE); (s)