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Proof step 61 from proof refine-remap (previous step)

# avol0 = # lpt + m5, # avol0 = n0 + m5, avol0[m1] = mapped(buf1), avol0[m2] = mapped(buf0), avol0[0] = mapped(buf), avol1 = subarray(avol0, m5, # lpt), m6 < # lpt, disk-layout(mksb(adr, m0, m1, m2, m3, m4, m5), # lpt), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m5, # lpt)), is-encoded(log, buf1), is-encoded(lpt, lebs(avol0, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m0, m1, m2, m3, m4, m5), buf), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol0, m4, lptlebs(# lpt, LEB_SIZE)), m5 ≤ # avol0, ⌊err0⌋ , logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟨apersistence_io_remap#(m6, adr, m0, log, lpt, orphans; avol1; err1)⟩ ( avol1 = subarray(avol0[m5 + m6, unmapped], m5, n0) ∧ is-encoded(log, avol0[m5 + m6, unmapped][m1].data) ∧ is-encoded(lpt, lebs(avol0[m5 + m6, unmapped], m4, lptlebs(n0, LEB_SIZE))) ∧ is-encoded-pad(orphans, m3, avol0[m2].data) ∧ err0 = err1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: subarray-avol-write: n < m ⊦ # avol = main + m → subarray(avol[main + n, aleb], main, m) = subarray(avol, main, m)[n, aleb];%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%n + m ≤ n0, n + m ≤ # avol ⊦ lebs(avol[n0, aleb], n, m) = lebs(avol, n, m); (s)%⊦ disk-layout(mksb(adr, m0, m1, m2, m, m3, m4), mainareasize) → ¬ m4 + n < m3 + lptlebs(mainareasize, LEB_SIZE); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)