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

# avol = # lpt0 + m5, avol[m0] = mapped(buf1), avol[m1] = mapped(buf0), avol[0] = mapped(buf), avol0 = subarray(avol, m5, # lpt0), avol1 = avol, disk-layout(mksb(adr, m, m0, m1, m3, m4, m5), # lpt0), ebm-vol-inv(subarray(avol, m5, # lpt0)), ebm-vol-inv(avol), is-encoded(mksb(adr, m, m0, m1, m3, m4, m5), buf), is-encoded(lpt0, lebs(avol, m4, lptlebs(# lpt0, LEB_SIZE))), is-encoded(plog, buf1), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol, m4, lptlebs(# lpt0, LEB_SIZE)), m5 ≤ # avol, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ∀ logoff, avol, err. (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ebm-vol-inv(avol) ∧ subarray(avol, m5, # lpt0) = subarray(avol1, m5, # lpt0) ∧ ( err = ESUCCESS → m5 + # lpt0 = # avol ∧ avol[0].mapped? ∧ is-encoded(mksb(adr, m, m0, m1, m3, m4, m5), avol[0].data) ∧ avol[m1].mapped? ∧ is-encoded-pad(orphans, m3, avol[m1].data) ∧ avol[m0].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m0].data = logoff) ∧ is-encoded(plog + m2 ', avol[m0].data) ∧ mapped-full?(avol, m4, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, m4, lptlebs(# lpt0, LEB_SIZE)))) ∧ ( err ≠ ESUCCESS → m5 + # lpt0 = # avol ∧ avol[0].mapped? ∧ is-encoded(mksb(adr, m, m0, m1, m3, m4, m5), avol[0].data) ∧ avol[m1].mapped? ∧ is-encoded-pad(orphans, m3, avol[m1].data) ∧ avol[m0].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m0].data = logoff) ∧ is-encoded(plog, avol[m0].data) ∧ mapped-full?(avol, m4, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, m4, lptlebs(# lpt0, LEB_SIZE)))) → ⟨apersistence_io_add_log_leb#(m2, adr, m, avol0, lpt0, orphans; plog; err0)⟩ ( # avol = m5 + (# avol - m5) ∧ avol0 = subarray(avol, m5, # avol - m5) ∧ is-encoded(plog, avol[m0].data) ∧ is-encoded(lpt0, lebs(avol, m4, lptlebs(# avol - m5, LEB_SIZE))) ∧ is-encoded-pad(orphans, m3, avol[m1].data) ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
# avol = # lpt0 + m5, avol[0] = mapped(buf), avol[m1] = mapped(buf0), avol[m0] = mapped(buf1), subarray(avol2, m5, # lpt0) = subarray(avol, m5, # lpt0), disk-layout(mksb(adr, m, m0, m1, m3, m4, m5), # lpt0), ebm-vol-inv(avol2), ebm-vol-inv(avol), ebm-vol-inv(subarray(avol, m5, # lpt0)), is-encoded(plog, buf1), is-encoded(lpt0, lebs(avol, m4, lptlebs(# lpt0, LEB_SIZE))), is-encoded(mksb(adr, m, m0, m1, m3, m4, m5), buf), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol, m4, lptlebs(# lpt0, LEB_SIZE)), m5 ≤ # avol, err = ESUCCESS → # avol = # avol2 ∧ avol2[0].mapped? ∧ is-encoded(mksb(adr, m, m0, m1, m3, m4, m5), avol2[0].data) ∧ avol2[m1].mapped? ∧ is-encoded-pad(orphans, m3, avol2[m1].data) ∧ avol2[m0].mapped? ∧ (logoff0 ≠ LEB_SIZE → # avol2[m0].data = logoff0) ∧ is-encoded(plog + m2 ', avol2[m0].data) ∧ mapped-full?(avol2, m4, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol2, m4, lptlebs(# lpt0, LEB_SIZE))), err ≠ ESUCCESS → # avol = # avol2 ∧ avol2[0].mapped? ∧ is-encoded(mksb(adr, m, m0, m1, m3, m4, m5), avol2[0].data) ∧ avol2[m1].mapped? ∧ is-encoded-pad(orphans, m3, avol2[m1].data) ∧ avol2[m0].mapped? ∧ (logoff0 ≠ LEB_SIZE → # avol2[m0].data = logoff0) ∧ is-encoded(plog, avol2[m0].data) ∧ mapped-full?(avol2, m4, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol2, m4, lptlebs(# lpt0, LEB_SIZE))), logoff ≠ LEB_SIZE → # buf1 = logoff, err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟨apersistence_io_add_log_leb#(m2, adr, m, subarray(avol, m5, # lpt0), lpt0, orphans; plog; err0)⟩ ( # avol2 = m5 + (# avol2 - m5) ∧ subarray(avol, m5, # lpt0) = subarray(avol2, m5, # avol2 - m5) ∧ is-encoded(plog, avol2[m0].data) ∧ is-encoded(lpt0, lebs(avol2, m4, lptlebs(# avol2 - m5, LEB_SIZE))) ∧ is-encoded-pad(orphans, m3, avol2[m1].data) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic