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Proof step 109 from proof inv-format (previous step)

# avol = # avol0, # lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE)) = lptsize(# lpt, LEB_SIZE), # avol0 = # lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE), avol[0] = mapped(buf), avol0[4] = fill(mkavolume(# avol0), unmapped)[4], avol0[3] = mapped(mkbuf(0)), avol0[2] = fill(mkavolume(# avol0), unmapped)[2], avol0[1] = mapped(mkbuf(0)), avol0[0] = fill(mkavolume(# avol0), unmapped)[0], ebm-vol-inv(fill(mkavolume(# avol0), unmapped)[1, mapped(mkbuf(0))][3, mapped(mkbuf(0))]), ebm-vol-inv(fill(mkavolume(# avol0), unmapped)), ebm-vol-inv(fill(mkavolume(# avol0), unmapped)[1, mapped(mkbuf(0))]), ebm-vol-inv(avol0), ebm-vol-inv(avol), id○(avol, avol0, 0), is-encoded(((((((sb0.indexaddr:= adr).maxino:= m1).log:= 1).orph:= 3).orphsize:= 0).lpt:= 5).main:= (5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf), is-encoded(lpt, lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE))), mapped-full?(avol0, 5, lptlebs(# lpt, LEB_SIZE)), range= (avol0, 5 + lptlebs(# lpt, LEB_SIZE), fill(mkavolume(# avol0), unmapped), 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE) + # lpt), 5 ≤ # avol0, 5 + lptlebs(# lpt, LEB_SIZE) ≤ # avol0 ⊦ (∃ lpt0, log, orphans. disk-layout (((((((sb0.indexaddr:= adr).maxino:= m1).log:= 1).orph:= 3).orphsize:= 0).lpt:= 5).main:= (5 + 2 * lptlebs(# lpt, LEB_SIZE)), # lpt0) ∧ (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt0 = # avol0 ∧ avol[3].mapped? ∧ is-encoded-pad(orphans, 0, avol[3].data) ∧ avol[1].mapped? ∧ is-encoded(log, avol[1].data) ∧ mapped-full?(avol0, 5, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, 5, lptlebs(# lpt0, LEB_SIZE)))) ∧ subarray(avol0, 5 + 2 * lptlebs(# lpt, LEB_SIZE), # avol0 - 5 + 2 * lptlebs(# lpt, LEB_SIZE)) = fill(mkavolume(# lpt), unmapped) ∧ is-encoded(lpt, lebs(avol, 5, lptlebs(# avol0 - 5 + 2 * lptlebs(# lpt, LEB_SIZE), LEB_SIZE))) ∧ avol[1].data = mkbuf(0) ∧ avol[3].data = mkbuf(0)

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] → [5 + 2 * lptlebs(# lpt, LEB_SIZE), # avol0, n]

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m + n = m + n0 ↔ n = n0; (s)%n < n0 ⊦ (* n) ≠ m0 + (* n0); (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ 2 * m = 0 ↔ m = 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m0 ≠ 0 → (m0 < m0 * m ↔ 1 < m); (s)% ⊦ ¬ m + n < m; (s)%n < m0, m0 + m1 ≤ # avol1 ⊦ id○(avol1, avol0, n) → lebs(avol1, m0, m1) = lebs(avol0, m0, m1); (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: 5 + 2 * lptlebs(# lpt, LEB_SIZE), # avol0, n