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Proof step 125 from proof refine-write (previous step)

# avol0 = # lpt + m6, avol0[m2] = mapped(buf3), avol0[m3] = mapped(buf2), avol0[0] = mapped(buf1), avol0[m6 + m8] = mapped(buf0), avol = avol0, err = err0, m = m7, m0 = m6 + m8, n0 = n, n1 = n2, m8 < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m6, # lpt)), is-aligned(n, EB_PAGE_SIZE), is-aligned(m7, EB_PAGE_SIZE), is-encoded(log, buf3), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf1), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), n2 + n ≤ # buf, # buf0 ≤ m7, m6 ≤ # avol0, m7 + n ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf3 = logoff, ∀ n3. ¬(n3 < n0 ∧ is-aligned(n3, EB_PAGE_SIZE)), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟨avol1 := subarray(avol0, m6, # lpt); apersistence_io_write#(m8, m7, n2, n, buf, adr, m1, log, lpt, orphans; avol1; err1)⟩ ( # avol = m6 + (# avol - m6) ∧ avol1 = subarray(avol, m6, # avol - m6) ∧ is-encoded(log, avol[m2].data) ∧ is-encoded(lpt, lebs(avol, m5, lptlebs(# avol - m6, LEB_SIZE))) ∧ is-encoded-pad(orphans, m4, avol[m3].data) ∧ err = err1), err = ESUCCESS

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 126:
# avol0 = # lpt + m6, avol0[m6 + m8] = mapped(buf0), avol0[0] = mapped(buf1), avol0[m3] = mapped(buf2), avol0[m2] = mapped(buf3), avol = avol0, avol1 = subarray(avol0, m6, # lpt), err = err0, m = m7, m0 = m6 + m8, n0 = n, n1 = n2, m8 < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(subarray(avol0, m6, # lpt)), ebm-vol-inv(avol0), is-aligned(m7, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf1), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf3), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), m7 + n ≤ LEB_SIZE, m6 ≤ # avol0, # buf0 ≤ m7, n2 + n ≤ # buf, m6 + # lpt ≤ # avol0, logoff ≠ LEB_SIZE → # buf3 = logoff, ∀ n3. ¬(n3 < n0 ∧ is-aligned(n3, EB_PAGE_SIZE)), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟨apersistence_io_write#(m8, m7, n2, n, buf, adr, m1, log, lpt, orphans; avol1; err1)⟩ ( # avol = m6 + (# avol - m6) ∧ avol1 = subarray(avol, m6, # avol - m6) ∧ is-encoded(log, avol[m2].data) ∧ is-encoded(lpt, lebs(avol, m5, lptlebs(# avol - m6, LEB_SIZE))) ∧ is-encoded-pad(orphans, m4, avol[m3].data) ∧ err = err1), err = ESUCCESS

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)%c: ⊦ m + n = n + m; from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n → ¬ n < m; (s)