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Proof step 6 from proof refine-read (previous step)

# lpt = n1, # avol0 = n1 + m6, m6 + # lpt0 = # avol0, avol0[m2] = mapped(buf4), avol0[m3] = mapped(buf3), avol0[0] = mapped(buf2), subarray(avol0, m6, # lpt)[m] = mapped(buf1), buf = buf0, m < # lpt0, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt0), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m6, # lpt)), is-encoded(lpt0, lebs(avol0, m5, lptlebs(# lpt0, LEB_SIZE))), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf2), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf4), is-encoded-pad(orphans, m4, buf3), mapped-full?(avol0, m5, lptlebs(# lpt0, LEB_SIZE)), m0 + n0 ≤ LEB_SIZE, n + n0 ≤ # buf0, m6 ≤ # avol0, logoff ≠ LEB_SIZE → # buf4 = logoff ⊦ ⟪persistence_io_read#(m, m0, n, n0, mksb(adr, m1, m2, m3, m4, m5, m6), avol0; buf; err)⟫ ⟨apersistence_io_read#(m, m0, n, n0, adr, m1, log, subarray(avol0, m6, n1), lpt, orphans; buf0; err0)⟩ (buf = buf0 ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
# avol0 = # lpt + m6, avol0[0] = mapped(buf2), avol0[m3] = mapped(buf3), avol0[m2] = mapped(buf4), avol0[m6 + m] = mapped(buf1), buf = buf0, m < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(subarray(avol0, m6, # lpt)), ebm-vol-inv(avol0), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf2), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf4), is-encoded-pad(orphans, m4, buf3), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), m6 ≤ # avol0, n + n0 ≤ # buf0, m0 + n0 ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf4 = logoff ⊦ ⟪persistence_io_read#(m, m0, n, n0, mksb(adr, m1, m2, m3, m4, m5, m6), avol0; buf; err)⟫ ⟨apersistence_io_read#(m, m0, n, n0, adr, m1, log, subarray(avol0, m6, # lpt), lpt, orphans; buf0; err0)⟩ (buf = buf0 ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%⊦ is-encoded(lpt0, buf) ∧ # lpt0 = # lpt1 → (is-encoded(lpt1, buf) ↔ lpt0 = lpt1); (s)% ⊦ n0 < n → subarray(avol, m, n)[n0] = avol[m + n0]; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%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