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Proof step 153 from proof inv-commit (previous step)

# avol1 = # avol0, # lpt0 = # lpt, (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt = # avol0, avol0[1] = mapped(buf1), avol0[3] = mapped(buf0), avol0[0] = mapped(buf), m0 = LEB_SIZE, sb0 = mksb(adr0, m2, 1, 3, m6, 5, 5 + 2 * lptlebs(# lpt, LEB_SIZE)), sb1 = mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)), 4 < # avol0, 2 < # avol0, ebm-vol-inv(avol1), ebm-vol-inv(avol0), ebm-vol-inv(avol0[2, mapped(mkbuf(0))]), id○(avol1, avol0[2, mapped(mkbuf(0))], 4), is-encoded(mksb(adr0, m2, 1, 3, m6, 5, 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf), is-encoded(lpt0, lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf1), is-encoded-pad(orphans0, m6, buf0), mapped-full?(avol0, 5, lptlebs(# lpt, LEB_SIZE)), 5 + 2 * lptlebs(# lpt, LEB_SIZE) ≤ # avol0, err = ESUCCESS → avol1[4].mapped? ∧ is-encoded-pad(orphans, # orphans, avol1[4].data), logoff ≠ LEB_SIZE → # buf1 = logoff, err = ESUCCESS ∨ ⌊err⌋ ⊦ err = ESUCCESS, (∃ lpt1, log, orphans. disk-layout(sb0, # lpt1) ∧ sb0.main + # lpt1 = # avol1 ∧ avol1[0].mapped? ∧ is-encoded(sb0, avol1[0].data) ∧ avol1[sb0.orph].mapped? ∧ is-encoded-pad(orphans, sb0.orphsize, avol1[sb0.orph].data) ∧ avol1[sb0.log].mapped? ∧ (logoff ≠ LEB_SIZE → # avol1[sb0.log].data = logoff) ∧ is-encoded(log, avol1[sb0.log].data) ∧ mapped-full?(avol1, sb0.lpt, lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol1, sb0.lpt, lptlebs(# lpt1, LEB_SIZE)))) ∧ ebm-vol-inv(avol1) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → sb0.indexaddr = adr ∧ sb0.maxino = m3 ∧ avol1[sb0.log].data = mkbuf(0) ∧ is-encoded(lpt, lebs(avol1, sb0.lpt, lptlebs(# avol1 - sb0.main, LEB_SIZE))) ∧ is-encoded-pad(orphans, sb0.orphsize, avol1[sb0.orph].data)) ∧ ( err ≠ ESUCCESS → sb0 = mksb(adr0, m2, 1, 3, m6, 5, sb0.main) ∧ avol1[1] = avol0[1] ∧ avol1[3] = avol0[3] ∧ lebs(avol1, 5, lptlebs(# avol1 - sb0.main, LEB_SIZE)) = lebs(avol0, 5, lptlebs(# avol1 - sb0.main, LEB_SIZE))) ∧ sb0.main = 5 + 2 * lptlebs(# lpt, LEB_SIZE) ∧ # avol1 = # avol0 ∧ subarray(avol1, sb0.main, # avol1 - sb0.main) = subarray(avol0, sb0.main, # avol1 - sb0.main)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: idcircle-concrete-write: n0 ≠ n, m ≠ n0, n0 < # avol ⊦ avol0[(* n0)] = aleb0 ∧ id○(avol, avol0[(* n), aleb], (* m)) → avol[(* n0)] = aleb0;%nat-stuff3: ⊦ n = 5 + n1 → n ≠ 1;%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);%n < n0 ⊦ subarray(avol[n, aleb], n0, n1) = subarray(avol, n0, n1); (s)%n < n0 ⊦ (* n) < m0 + (* n0); (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)% ⊦ is-encoded(nx0, buf) → (is-encoded(nx1, buf) ↔ nx0 = nx1); (s)% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)%⊦ is-encoded-pad(ns0, n, buf) → (is-encoded-pad(ns1, n, buf) ↔ ns0 = ns1); (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).orphsize = m2; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).log = m0; (s)%n0 < n ⊦ mapped-full?(avol[n0, aleb], n, m) ↔ mapped-full?(avol, n, m); (s)%n < m0 ⊦ id○(avol1, avol0, n) → (mapped-full?(avol1, m0, m1) ↔ mapped-full?(avol0, m0, m1)); (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).lpt = m3; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).orph = m1; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ 0 < m ↔ m ≠ 0; (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)