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Proof step 5 from proof refine-add-log-leb (previous step)

# lpt = # avol - m5, m5 + # lpt0 = # avol, avol[m0] = mapped(buf1), avol[m1] = mapped(buf0), avol[0] = mapped(buf), avol0 = subarray(avol, m5, # lpt), disk-layout(mksb(adr, m, m0, m1, m3, m4, m5), # lpt0), ebm-vol-inv(avol), ebm-vol-inv(subarray(avol, m5, # lpt)), is-encoded(lpt0, lebs(avol, m4, lptlebs(# lpt0, LEB_SIZE))), is-encoded(mksb(adr, m, m0, m1, m3, m4, m5), buf), is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(plog, buf1), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol, m4, lptlebs(# lpt0, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪persistence_io_add_log_leb#(m2, mksb(adr, m, m0, m1, m3, m4, m5), EB_PAGE_SIZE, LEB_SIZE; logoff, avol; err)⟫ ⟨apersistence_io_add_log_leb#(m2, adr, m, avol0, lpt, orphans; plog; err0)⟩ ( # avol = m5 + (# avol - m5) ∧ avol0 = subarray(avol, m5, # avol - m5) ∧ is-encoded(plog, avol[m0].data) ∧ is-encoded(lpt, lebs(avol, m4, lptlebs(# avol - m5, LEB_SIZE))) ∧ is-encoded-pad(orphans, m3, avol[m1].data) ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# avol, m5, n]

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: # avol, m5, n