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Proof step 31 from proof inv-format (previous step)

# wlar = # apebs0, # apebs0 = n0 + vtblpnum0, vtblpnum0 < # apebs0, ubi-io-initial(apebs0), vtblpnum2 ≤ # apebs0, vtblpnum0 ≤ # apebs0, vtblpnum2 ≠ # apebs0 → ¬ apebs0[vtblpnum2].bad, ∀ n3. n3 < vtblpnum0 → (apebs0[n3].bad → wlar[n3] = wl-entry(0, erroneous)) ∧ (¬ apebs0[n3].bad → apebs0[n3].echdr.valid? ∧ wlar[n3] = wl-entry(apebs0[n3].echdr.ec, free) ∧ apebs0[n3].vidhdr = empty) ⊦ ⟪aubi_io_isbad#(vtblpnum0, apebs0; ; isbad, err0); vtblpnum := vtblpnum0; n := # apebs0; if err0 = ESUCCESS then if ¬ isbad then let aehdr = ?, bitflips = ? in {aubi_io_read_echdr#(vtblpnum, apebs0; aehdr; bitflips, err0); if err0 = ESUCCESS ∧ vtblpnum2 = n then vtblpnum2 := vtblpnum; if err0 = ESUCCESS ∧ aehdr.valid? then wlar[vtblpnum] := wl-entry(aehdr.ec, free)} else wlar[vtblpnum] := wl-entry(0, erroneous); vtblpnum := vtblpnum + 1⟫ ( vtblpnum ≤ # apebs0 ∧ n = # apebs0 ∧ # wlar = # apebs0 ∧ (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ ( err0 = ESUCCESS → vtblpnum2 ≤ # apebs0 ∧ (∀ n3. n3 < vtblpnum → (apebs0[n3].bad → wlar[n3] = wl-entry(0, erroneous)) ∧ (¬ apebs0[n3].bad → apebs0[n3].echdr.valid? ∧ wlar[n3] = wl-entry(apebs0[n3].echdr.ec, free) ∧ apebs0[n3].vidhdr = empty)) ∧ (vtblpnum2 ≠ # apebs0 → ¬ apebs0[vtblpnum2].bad)) ∧ # apebs0 < n0 + vtblpnum)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
# apebs0 = n0 + vtblpnum0, # wlar = n0 + vtblpnum0, n0 ≠ 0, ubi-io-initial(apebs0), vtblpnum2 ≤ n0 + vtblpnum0, vtblpnum2 ≠ n0 + vtblpnum0 → ¬ apebs0[vtblpnum2].bad, ∀ n3. n3 < vtblpnum0 → (apebs0[n3].bad → wlar[n3] = wl-entry(0, erroneous)) ∧ (¬ apebs0[n3].bad → apebs0[n3].echdr.valid? ∧ wlar[n3] = wl-entry(apebs0[n3].echdr.ec, free) ∧ apebs0[n3].vidhdr = empty) ⊦ ⟪aubi_io_isbad#(vtblpnum0, apebs0; ; isbad, err0); vtblpnum := vtblpnum0; n := # apebs0; if err0 = ESUCCESS then if ¬ isbad then let aehdr = ?, bitflips = ? in {aubi_io_read_echdr#(vtblpnum, apebs0; aehdr; bitflips, err0); if err0 = ESUCCESS ∧ vtblpnum2 = n then vtblpnum2 := vtblpnum; if err0 = ESUCCESS ∧ aehdr.valid? then wlar[vtblpnum] := wl-entry(aehdr.ec, free)} else wlar[vtblpnum] := wl-entry(0, erroneous); vtblpnum := vtblpnum + 1⟫ ( vtblpnum ≤ # apebs0 ∧ n = # apebs0 ∧ # wlar = # apebs0 ∧ (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ ( err0 = ESUCCESS → vtblpnum2 ≤ # apebs0 ∧ (∀ n3. n3 < vtblpnum → (apebs0[n3].bad → wlar[n3] = wl-entry(0, erroneous)) ∧ (¬ apebs0[n3].bad → apebs0[n3].echdr.valid? ∧ wlar[n3] = wl-entry(apebs0[n3].echdr.ec, free) ∧ apebs0[n3].vidhdr = empty)) ∧ (vtblpnum2 ≠ # apebs0 → ¬ apebs0[vtblpnum2].bad)) ∧ # apebs0 < n0 + vtblpnum)

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → m ≤ n; (s)