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Proof step 29 from proof prepost-scan-all (previous step)

bflipset0 = ∅, err = ESUCCESS, err0 = ESUCCESS, nx0 = [], q0 = [], recs0 = ∅, sqnum0 = 0, vtblpnum0 = vtblpnum, vtblpnum3 = LEB_SIZE, vtblpnum4 = 0, vtblpnum5 = 0, vtblpnum6 = 0, wlar0 = fill(mkwlarray(# apebs), wl-entry(0, free)), vtblpnum0 < # apebs, scan-all-inv(vtblpnum0, apebs, recs, wlar, q, bflipset, nx, sqnum, err), ubi-io-inv(apebs), unique-sqns(apebs) ⊦ ⟪aubi_io_isbad#(vtblpnum0, apebs; ; isbad, err); if err = ESUCCESS then if isbad then wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, erroneous) else let aehdr = ?, bitflips = ? in {aubi_io_read_echdr#(vtblpnum0, apebs; aehdr; bitflips, err); if err = ESUCCESS then if ¬ aehdr.valid? then {nx := vtblpnum0 ' + nx; wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, erasing); q := q + eq-entry(vtblpnum0, none) '} else let avhdr = ? in {vtblpnum2 := vtblpnum2 + 1; vtblpnum1 := vtblpnum1 + aehdr.ec; wlar[vtblpnum0].ec := aehdr.ec; aubi_io_read_vidhdr#(vtblpnum0, apebs; avhdr; bitflips, err); if err = ESUCCESS then if avhdr = empty then if bitflips then {wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, erasing); q := q + eq-entry(vtblpnum0, none) '} else wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, free) else if avhdr.valid? then let buf = mkbuf(vtblpnum3) in {if avhdr.size ≠ 0 then let boolvar = ? in {aubi_io_read_data#(vtblpnum0, 0, 0, vtblpnum3, apebs; buf; boolvar, err); bitflips := bitflips ∨ boolvar}; if err = ESUCCESS then let ladr = avhdr.vol × avhdr.leb, n = 0 in {if ladr ∈ recs then n := recs[ladr].sqn; if avhdr.size ≠ 0 → avhdr.size ≤ datasize(buf) ∧ avhdr.checksum = checksum(buf, avhdr.size) then {sqnum := max(sqnum, avhdr.sqn + 1); if n ≤ avhdr.sqn then {wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, used); if bitflips then bflipset := bflipset ++ vtblpnum0; if ladr ∈ recs then let vtblpnum = recs[ladr].pnum in {bflipset := bflipset -- vtblpnum; wlar[vtblpnum] := wl-entry(wlar[vtblpnum].ec, erasing); q := q + eq-entry(vtblpnum, avhdr.vol × avhdr.leb) '}; recs[ladr] := recovery-entry(vtblpnum0, avhdr.sqn)} else {wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, erasing); q := q + eq-entry(vtblpnum0, ladr.vol × ladr.leb) '}} else {wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, erasing); q := q + eq-entry(vtblpnum0, none) '}}} else {wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, erasing); q := q + eq-entry(vtblpnum0, none) '}}}; vtblpnum0 := vtblpnum0 + 1⟫ (scan-all-inv(vtblpnum0, apebs, recs, wlar, q, bflipset, nx, sqnum, err) ∧ # apebs - vtblpnum0 < # apebs - vtblpnum)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
# apebs = # wlar, nx < vtblpnum, vtblpnum < # wlar, bflipset-cons(bflipset, subarray(wlar, 0, vtblpnum)), indices-erasing(wlar, nx), ubi-io-inv(apebs), unique-sqns(apebs), valid-eraseq(subarray(wlar, 0, vtblpnum), q), valid-eraseq-stronger(subarray(apebs, 0, vtblpnum), q), valid-global-sqn(subarray(apebs, 0, vtblpnum), sqnum), valid-recs(subarray(apebs, 0, vtblpnum), subarray(wlar, 0, vtblpnum), recs), valid-recs-sqns(apebs, recs), valid-wl(subarray(apebs, 0, vtblpnum), subarray(wlar, 0, vtblpnum)), ¬ dups(nx) ⊦ ⟪aubi_io_isbad#(vtblpnum, apebs; ; isbad, err); vtblpnum0 := vtblpnum; if err = ESUCCESS then if isbad then wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, erroneous) else let aehdr = ?, bitflips = ? in {aubi_io_read_echdr#(vtblpnum0, apebs; aehdr; bitflips, err); if err = ESUCCESS then if ¬ aehdr.valid? then {nx := vtblpnum0 ' + nx; wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, erasing); q := q + eq-entry(vtblpnum0, none) '} else let avhdr = ? in {vtblpnum2 := vtblpnum2 + 1; vtblpnum1 := vtblpnum1 + aehdr.ec; wlar[vtblpnum0].ec := aehdr.ec; aubi_io_read_vidhdr#(vtblpnum0, apebs; avhdr; bitflips, err); if err = ESUCCESS then if avhdr = empty then if bitflips then {wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, erasing); q := q + eq-entry(vtblpnum0, none) '} else wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, free) else if avhdr.valid? then let buf = mkbuf(LEB_SIZE) in {if avhdr.size ≠ 0 then let boolvar = ? in {aubi_io_read_data#(vtblpnum0, 0, 0, LEB_SIZE, apebs; buf; boolvar, err); bitflips := bitflips ∨ boolvar}; if err = ESUCCESS then let ladr = avhdr.vol × avhdr.leb, n = 0 in {if ladr ∈ recs then n := recs[ladr].sqn; if avhdr.size ≠ 0 → avhdr.size ≤ datasize(buf) ∧ avhdr.checksum = checksum(buf, avhdr.size) then {sqnum := max(sqnum, avhdr.sqn + 1); if n ≤ avhdr.sqn then {wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, used); if bitflips then bflipset := bflipset ++ vtblpnum0; if ladr ∈ recs then let vtblpnum = recs[ladr].pnum in {bflipset := bflipset -- vtblpnum; wlar[vtblpnum] := wl-entry(wlar[vtblpnum].ec, erasing); q := q + eq-entry(vtblpnum, avhdr.vol × avhdr.leb) '}; recs[ladr] := recovery-entry(vtblpnum0, avhdr.sqn)} else {wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, erasing); q := q + eq-entry(vtblpnum0, ladr.vol × ladr.leb) '}} else {wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, erasing); q := q + eq-entry(vtblpnum0, none) '}}} else {wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, erasing); q := q + eq-entry(vtblpnum0, none) '}}}; vtblpnum0 := vtblpnum0 + 1⟫ ( vtblpnum0 ≤ # apebs ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → # apebs = # wlar ∧ ¬ dups(nx) ∧ nx < vtblpnum0 ∧ indices-erasing(wlar, nx) ∧ valid-global-sqn(subarray(apebs, 0, vtblpnum0), sqnum) ∧ valid-eraseq(subarray(wlar, 0, vtblpnum0), q) ∧ bflipset-cons(bflipset, subarray(wlar, 0, vtblpnum0)) ∧ valid-eraseq-stronger(subarray(apebs, 0, vtblpnum0), q) ∧ valid-wl(subarray(apebs, 0, vtblpnum0), subarray(wlar, 0, vtblpnum0)) ∧ valid-recs-sqns(apebs, recs) ∧ valid-recs(subarray(apebs, 0, vtblpnum0), subarray(wlar, 0, vtblpnum0), recs)) ∧ # apebs < (# apebs - vtblpnum) + vtblpnum0)

Rule argument

Additional information

Used simplifier rules: ⊦ 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%n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < n → m ≤ n; (s)%⊦ scan-all-inv(n, apebs, recs, wlar, q, bflipset, nx, n1, err) ↔ ¬ ¬ ( n ≤ # apebs ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → ubi-io-inv(apebs) ∧ unique-sqns(apebs) ∧ # apebs = # wlar ∧ ¬ dups(nx) ∧ nx < n ∧ indices-erasing(wlar, nx) ∧ valid-global-sqn(subarray(apebs, 0, n), n1) ∧ valid-eraseq(subarray(wlar, 0, n), q) ∧ bflipset-cons(bflipset, subarray(wlar, 0, n)) ∧ valid-eraseq-stronger(subarray(apebs, 0, n), q) ∧ valid-wl(subarray(apebs, 0, n), subarray(wlar, 0, n)) ∧ valid-recs-sqns(apebs, recs) ∧ valid-recs (subarray(apebs, 0, n), subarray(wlar, 0, n), recs))); (s)