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Proof step 11 from proof inv-add-log-leb (previous step)

m5 + # lpt = # avol, avol[m0] = mapped(buf1), avol[m2] = mapped(buf0), avol[0] = mapped(buf), subarray(avol0, m5, # lpt) = subarray(avol, m5, # lpt), disk-layout(mksb(adr, m, m0, m2, m3, m4, m5), # lpt), ebm-vol-inv(avol), ebm-vol-inv(avol0), is-encoded(log, buf1), is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m, m0, m2, m3, m4, m5), buf), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol, m4, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff, err ≠ ESUCCESS → # avol = # avol0 ∧ avol0[0].mapped? ∧ is-encoded(mksb(adr, m, m0, m2, m3, m4, m5), avol0[0].data) ∧ avol0[m2].mapped? ∧ is-encoded-pad(orphans, m3, avol0[m2].data) ∧ avol0[m0].mapped? ∧ (logoff0 ≠ LEB_SIZE → # avol0[m0].data = logoff0) ∧ is-encoded(log, avol0[m0].data) ∧ mapped-full?(avol0, m4, lptlebs(# lpt, LEB_SIZE)) ∧ is-encoded(lpt, lebs(avol0, m4, lptlebs(# lpt, LEB_SIZE))), err = ESUCCESS ∨ ⌊err⌋ ⊦ err = ESUCCESS, ∃ lpt0, log, orphans. disk-layout(mksb(adr, m, m0, m2, m3, m4, m5), # lpt0) ∧ m5 + # lpt0 = # avol0 ∧ avol0[0].mapped? ∧ is-encoded(mksb(adr, m, m0, m2, m3, m4, m5), avol0[0].data) ∧ avol0[m2].mapped? ∧ is-encoded-pad(orphans, m3, avol0[m2].data) ∧ avol0[m0].mapped? ∧ (logoff0 ≠ LEB_SIZE → # avol0[m0].data = logoff0) ∧ is-encoded(log, avol0[m0].data) ∧ mapped-full?(avol0, m4, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol0, m4, lptlebs(# lpt0, LEB_SIZE)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
# avol = # avol0, m5 + # lpt = # avol0, avol0[m0] = mapped(buf4), avol0[m2] = mapped(buf3), avol0[0] = mapped(buf2), avol[m0] = mapped(buf1), avol[m2] = mapped(buf0), avol[0] = mapped(buf), subarray(avol0, m5, # lpt) = subarray(avol, m5, # lpt), disk-layout(mksb(adr, m, m0, m2, m3, m4, m5), # lpt), ebm-vol-inv(avol), ebm-vol-inv(avol0), is-encoded(mksb(adr, m, m0, m2, m3, m4, m5), buf2), is-encoded(log, buf1), is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m, m0, m2, m3, m4, m5), buf), is-encoded(lpt, lebs(avol0, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf4), is-encoded-pad(orphans, m3, buf3), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol, m4, lptlebs(# lpt, LEB_SIZE)), mapped-full?(avol0, m4, lptlebs(# lpt, LEB_SIZE)), ⌊err⌋ , logoff ≠ LEB_SIZE → # buf1 = logoff, logoff0 ≠ LEB_SIZE → # buf4 = logoff0 ⊦ ∃ lpt0. m5 + # lpt0 = # avol0 ∧ mapped-full?(avol0, m4, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol0, m4, lptlebs(# lpt0, LEB_SIZE)))

Rule argument

Additional information

Used simplifier rules: m = n ⊦ disk-layout(sb, m) → disk-layout(sb, n); (s)%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ mapped(buf).mapped?; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ 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)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)