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Proof step 24 from proof inv-format (previous step)

# pebs0 = # pebs, m1 < # pebs, mtd-cons(pebs), mtd-cons(pebs0), ubi-io-initial(subarray(pebs, 0, m1)) ⊦ ⟪mtd_asm_isbad#(m1, pebs; ; isbad, err); m := m1; if err = ESUCCESS ∧ ¬ isbad then let aehdr = ?, bitflips = ? in {ubi_io_read_echdr#(m, EB_PAGE_SIZE, pebs; aehdr; bitflips, err); let n = (err = ESUCCESS ∧ aehdr.valid? ⊃ aehdr.ec + 1;0) in {mtd_asm_erase#(m; pebs; err); if err = ESUCCESS then ubi_io_write_echdr#(m, aechdr(n), EB_PAGE_SIZE; pebs; err)}}; m := m + 1⟫ ( m ≤ # pebs0 ∧ # pebs0 = # pebs ∧ mtd-cons(pebs) ∧ (err = ESUCCESS → ubi-io-initial(subarray(pebs, 0, m))) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # pebs0 < (# pebs0 - m1) + m)

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] → [# pebs0, m1, n0]

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ m +1 = m + 1; (s)% ⊦ m < n → ¬ n < m; (s)%# pebs = n ⊦ subarray(pebs, 0, n) = pebs; (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: # pebs0, m1, n0