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Proof step 5 from proof refine-read (previous step)

# lpt = # avol0 - m6, m6 + # lpt0 = # avol0, subarray(avol0, m6, # lpt)[m] = mapped(buf1), avol0[0] = mapped(buf2), avol0[m3] = mapped(buf3), avol0[m2] = mapped(buf4), buf = buf0, m < # lpt0, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt0), ebm-vol-inv(subarray(avol0, m6, # lpt)), ebm-vol-inv(avol0), is-encoded(log, buf4), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf2), is-encoded(lpt0, lebs(avol0, m5, lptlebs(# lpt0, LEB_SIZE))), is-encoded-pad(orphans, m4, buf3), mapped-full?(avol0, m5, lptlebs(# lpt0, LEB_SIZE)), 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, # avol0 - m6), lpt, orphans; buf0; err0)⟩ (buf = buf0 ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
# 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)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# avol0, m6, n1]

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # avol0, m6, n1