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Proof step 152 from proof inv-recover (previous step)

# lebs(avol1, m7, lptlebs(# lpt0, LEB_SIZE)) = lptsize(# lpt0, LEB_SIZE), m8 + # lpt0 = # avol1, avol1[0] = mapped(buf2), avol1[m5] = mapped(buf0), avol1[m10] = mapped(buf1), err0 = ESUCCESS, m0 = LEB_SIZE, sb = mksb(adr0, m9, m10, m5, m6, m7, m8), m10 < # avol2, disk-layout(mksb(adr0, m9, m10, m5, m6, m7, m8), # lpt0), ebm-vol-inv(avol1), is-encoded(mksb(adr0, m9, m10, m5, m6, m7, m8), buf2), is-encoded(log0, buf1), is-encoded(lpt0, lebs(avol1, m7, lptlebs(# lpt0, LEB_SIZE))), is-encoded-pad(orphans0, m6, buf0), mapped-full?(avol1, m7, lptlebs(# lpt0, LEB_SIZE)), m8 ≤ # avol1, m7 + lptlebs(# lpt0, LEB_SIZE) ≤ # avol1, avol1 ⊆ avol2, err0 = ESUCCESS → lpt0 = lpt1, m3 ≠ LEB_SIZE → # buf1 = m3, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ ( err0 = ESUCCESS → (∃ lpt1, log1, orphans1. disk-layout(sb, # lpt1) ∧ sb.main + # lpt1 = # avol1 ∧ is-encoded(sb, buf2) ∧ avol2[sb.orph].mapped? ∧ is-encoded-pad(orphans1, sb.orphsize, avol2[sb.orph].data) ∧ avol2[sb.log].mapped? ∧ (m0 ≠ LEB_SIZE → # avol2[sb.log].data = m0) ∧ is-encoded(log1, avol2[sb.log].data) ∧ mapped-full?(avol2, sb.lpt, lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol2, sb.lpt, lptlebs(# lpt1, LEB_SIZE)))) ∧ m0 = LEB_SIZE) ∧ (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ ( err0 = ESUCCESS → sb.indexaddr = adr0 ∧ sb.maxino = m9 ∧ # lpt1 = # lpt0 ∧ is-encoded(lpt1, lebs(avol2, m7, lptlebs(# lpt1, LEB_SIZE))) ∧ lebs(avol2, m7, lptlebs(# lpt1, LEB_SIZE)) = lebs(avol1, m7, lptlebs(# lpt1, LEB_SIZE)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: avol-down-mapped-eq: n < # avol0 ⊦ avol0 ⊆ avol1 ∧ avol0[n] = mapped(buf) ∧ ebm-vol-inv(avol0) → avol1[n] = mapped(buf);% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%m = n ⊦ disk-layout(sb, m) → disk-layout(sb, n); (s)%n + m ≤ # avol0 ⊦ mapped-full?(avol0, n, m) ∧ avol0 ⊆ avol1 → lebs(avol1, n, m) = lebs(avol0, n, m); (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).maxino = m; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).indexaddr = adr; (s)% ⊦ is-encoded(nx0, buf) → (is-encoded(nx1, buf) ↔ nx0 = nx1); (s)% ⊦ avol0 ⊆ avol1 → ¬ # avol0 < # avol1; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).lpt = m3; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).log = m0; (s)%⊦ is-encoded-pad(ns0, n, buf) → (is-encoded-pad(ns1, n, buf) ↔ ns0 = ns1); (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).orphsize = m2; (s)% ⊦ mapped(buf).mapped?; (s)%⊦ m6 + # lpt = # avol ∧ disk-layout(mksb(adr0, m1, m2, m3, m4, m5, m6), # lpt) → ¬ # avol ≤ m3; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).orph = m1; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).main = m4; (s)