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Proof step 13 from proof refine-add-log-leb (previous step)

# avol0 = # lpt0 + m5, avol0[m6] = mapped(buf1), avol0[m1] = mapped(buf0), avol0[0] = mapped(buf), avol = subarray(avol0, m5, # lpt0), lpt = lpt0, m0 = m2, ns = orphans, subarray(avol2, m5, # lpt0) = subarray(avol0, m5, # lpt0), disk-layout(mksb(adr, m, m6, m1, m3, m4, m5), # lpt0), ebm-vol-inv(subarray(avol0, m5, # lpt0)), ebm-vol-inv(avol0), ebm-vol-inv(avol2), is-encoded(mksb(adr, m, m6, m1, m3, m4, m5), buf), is-encoded(lpt0, lebs(avol0, m4, lptlebs(# lpt0, LEB_SIZE))), is-encoded(plog, buf1), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol0, m4, lptlebs(# lpt0, LEB_SIZE)), m5 + # lpt0 ≤ # avol0, m5 ≤ # avol0, logoff ≠ LEB_SIZE → # buf1 = logoff, 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))), 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 ∨ ⌊err1⌋ ⊦ ⟨fail_or_success#(; ; err); if err = ESUCCESS then plog := plog + m0⟩ ( # 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 14:
# avol0 = # lpt0 + m5, avol0[m6] = mapped(buf1), avol0[m1] = mapped(buf0), avol0[0] = mapped(buf), subarray(avol2, m5, # lpt0) = subarray(avol0, m5, # lpt0), disk-layout(mksb(adr, m, m6, m1, m3, m4, m5), # lpt0), ebm-vol-inv(subarray(avol0, m5, # lpt0)), ebm-vol-inv(avol0), ebm-vol-inv(avol2), is-encoded(mksb(adr, m, m6, m1, m3, m4, m5), buf), is-encoded(lpt0, lebs(avol0, m4, lptlebs(# lpt0, LEB_SIZE))), is-encoded(plog, buf1), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol0, m4, lptlebs(# lpt0, LEB_SIZE)), m5 ≤ # avol0, logoff ≠ LEB_SIZE → # buf1 = logoff, 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))), 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 ∨ ⌊err1⌋ ⊦ ⟨fail_or_success#(; ; err); if err = ESUCCESS then plog := plog + m2 '⟩ ( # 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)

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ nx + n = nx + n '; (s)