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Proof step 24 from proof refine-add-log-leb (previous step)

# avol0 = # lpt0 + m5, avol0[0] = mapped(buf), avol0[m1] = mapped(buf0), avol0[m6] = mapped(buf1), err = err1, subarray(avol2, m5, # lpt0) = subarray(avol0, m5, # lpt0), disk-layout(mksb(adr, m, m6, m1, m3, m4, m5), # lpt0), ebm-vol-inv(avol2), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m5, # lpt0)), is-encoded(plog, buf1), is-encoded(lpt0, lebs(avol0, m4, lptlebs(# lpt0, LEB_SIZE))), is-encoded(mksb(adr, m, m6, m1, m3, m4, m5), buf), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol0, m4, lptlebs(# lpt0, LEB_SIZE)), m5 ≤ # avol0, err1 = ESUCCESS → # avol0 = # avol2 ∧ avol2[0].mapped? ∧ is-encoded(mksb(adr, m, m6, m1, m3, m4, m5), avol2[0].data) ∧ avol2[m1].mapped? ∧ is-encoded-pad(orphans, m3, avol2[m1].data) ∧ avol2[m6].mapped? ∧ (logoff0 ≠ LEB_SIZE → # avol2[m6].data = logoff0) ∧ is-encoded(plog + m2 ', avol2[m6].data) ∧ mapped-full?(avol2, m4, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol2, m4, lptlebs(# lpt0, LEB_SIZE))), err1 ≠ ESUCCESS → # avol0 = # avol2 ∧ avol2[0].mapped? ∧ is-encoded(mksb(adr, m, m6, m1, m3, m4, m5), avol2[0].data) ∧ avol2[m1].mapped? ∧ is-encoded-pad(orphans, m3, avol2[m1].data) ∧ avol2[m6].mapped? ∧ (logoff0 ≠ LEB_SIZE → # avol2[m6].data = logoff0) ∧ is-encoded(plog, avol2[m6].data) ∧ mapped-full?(avol2, m4, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol2, m4, lptlebs(# lpt0, LEB_SIZE))), logoff ≠ LEB_SIZE → # buf1 = logoff, err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ err = ESUCCESS, # avol2 = m5 + (# avol2 - m5) ∧ subarray(avol0, m5, # lpt0) = subarray(avol2, m5, # avol2 - m5) ∧ is-encoded(plog, avol2[m6].data) ∧ is-encoded(lpt0, lebs(avol2, m4, lptlebs(# avol2 - m5, LEB_SIZE))) ∧ is-encoded-pad(orphans, m3, avol2[m1].data) ∧ err1 = err

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
# avol0 = # avol2, # avol2 = # lpt0 + m5, avol2[m6] = mapped(buf4), avol2[m1] = mapped(buf3), avol2[0] = mapped(buf2), avol0[0] = mapped(buf), avol0[m1] = mapped(buf0), avol0[m6] = mapped(buf1), subarray(avol2, m5, # lpt0) = subarray(avol0, m5, # lpt0), disk-layout(mksb(adr, m, m6, m1, m3, m4, m5), # lpt0), ebm-vol-inv(avol2), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m5, # lpt0)), is-encoded(mksb(adr, m, m6, m1, m3, m4, m5), buf2), is-encoded(plog, buf1), is-encoded(lpt0, lebs(avol0, m4, lptlebs(# lpt0, LEB_SIZE))), is-encoded(mksb(adr, m, m6, m1, m3, m4, m5), buf), is-encoded(lpt0, lebs(avol2, m4, lptlebs(# lpt0, LEB_SIZE))), is-encoded(plog, buf4), is-encoded-pad(orphans, m3, buf3), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol0, m4, lptlebs(# lpt0, LEB_SIZE)), mapped-full?(avol2, m4, lptlebs(# lpt0, LEB_SIZE)), m5 ≤ # avol2, ⌊err1⌋ , logoff ≠ LEB_SIZE → # buf1 = logoff, logoff0 ≠ LEB_SIZE → # buf4 = logoff0 ⊦ subarray(avol0, m5, # lpt0) = subarray(avol2, m5, # avol2 - m5) ∧ is-encoded(lpt0, lebs(avol2, m4, lptlebs(# avol2 - m5, LEB_SIZE)))

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf).data = buf; (s)%⊦ is-encoded-pad(ns0, n, buf) → (is-encoded-pad(ns1, n, buf) ↔ ns0 = ns1); (s)% ⊦ is-encoded(nx0, buf) → (is-encoded(nx1, buf) ↔ nx0 = nx1); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)