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Proof step 12 from proof initialization (previous step)

m9 + # lpt = # avol, avol[0] = mapped(buf), avol[m5] = mapped(mkbuf(0)), avol[m4] = mapped(mkbuf(0)), subarray(avol, m9, # avol - m9) = fill(mkavolume(# lpt0), unmapped), disk-layout(mksb(adr1, m3, m4, m5, 0, m8, m9), # lpt), ebm-vol-inv(avol), is-encoded(lpt, lebs(avol, m8, lptlebs(# lpt, LEB_SIZE))), is-encoded(lpt0, lebs(avol, m8, lptlebs(# avol - m9, LEB_SIZE))), is-encoded(mksb(adr1, m3, m4, m5, 0, m8, m9), buf), mapped-full?(avol, m8, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → 0 = logoff ⊦ ⟨apersistence_io_format#(# lpt0, LEB_SIZE, lpt0, adr1, m3; ; adr2, m6, plog, avol1, lpt1, ns0, err0)⟩ ( m6 = m3 ∧ adr2 = adr1 ∧ avol1 = subarray(avol, m9, # avol - m9) ∧ [] = plog ∧ is-encoded(lpt1, lebs(avol, m8, lptlebs(# avol - m9, LEB_SIZE))) ∧ ∅ = ns0 ∧ ESUCCESS = 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: [n, m, n0] → [m9, # avol, 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: m9, # avol, n