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Proof step 81 from proof prepost-scan-all (previous step)

# wlar = n0 + vtblpnum, # apebs = n0 + vtblpnum, apebs[vtblpnum] = mkpeb(aehdr, avhdr1, buf1, m0, false), aehdr = aechdr(m), aehdr.valid?, nx < vtblpnum, bflipset-cons(bflipset, subarray(wlar, 0, vtblpnum)), indices-erasing(wlar, nx), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr1, buf1, m0, false)), 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)) ⊦ ⟪aubi_io_read_vidhdr#(vtblpnum, apebs; avhdr; bitflips, err); wlar[vtblpnum].ec := m; if err = ESUCCESS then if avhdr = empty then if bitflips then {wlar[vtblpnum] := wl-entry(wlar[vtblpnum].ec, erasing); q := q + eq-entry(vtblpnum, none) '} else wlar[vtblpnum] := wl-entry(wlar[vtblpnum].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#(vtblpnum, 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[vtblpnum] := wl-entry(wlar[vtblpnum].ec, used); if bitflips then bflipset := bflipset ++ vtblpnum; if ladr ∈ recs then let vtblpnum0 = recs[ladr].pnum in {bflipset := bflipset -- vtblpnum0; wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, erasing); q := q + eq-entry(vtblpnum0, avhdr.vol × avhdr.leb) '}; recs[ladr] := recovery-entry(vtblpnum, avhdr.sqn)} else {wlar[vtblpnum] := wl-entry(wlar[vtblpnum].ec, erasing); q := q + eq-entry(vtblpnum, ladr.vol × ladr.leb) '}} else {wlar[vtblpnum] := wl-entry(wlar[vtblpnum].ec, erasing); q := q + eq-entry(vtblpnum, none) '}}} else {wlar[vtblpnum] := wl-entry(wlar[vtblpnum].ec, erasing); q := q + eq-entry(vtblpnum, none) '}; vtblpnum := vtblpnum + 1⟫ ( vtblpnum ≤ # apebs ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → # apebs = # wlar ∧ nx < vtblpnum ∧ indices-erasing(wlar, nx) ∧ valid-global-sqn(subarray(apebs, 0, vtblpnum), sqnum) ∧ valid-eraseq(subarray(wlar, 0, vtblpnum), q) ∧ bflipset-cons(bflipset, subarray(wlar, 0, vtblpnum)) ∧ valid-eraseq-stronger(subarray(apebs, 0, vtblpnum), q) ∧ valid-wl(subarray(apebs, 0, vtblpnum), subarray(wlar, 0, vtblpnum)) ∧ valid-recs-sqns(apebs, recs) ∧ valid-recs(subarray(apebs, 0, vtblpnum), subarray(wlar, 0, vtblpnum), recs)) ∧ # apebs < n0 + vtblpnum), n0 = 0, dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 82:
# apebs = n0 + vtblpnum, # wlar = n0 + vtblpnum, apebs[vtblpnum] = mkpeb(aechdr(m), avhdr1, buf1, m0, false), n0 ≠ 0, nx < vtblpnum, bflipset-cons(bflipset, subarray(wlar, 0, vtblpnum)), indices-erasing(wlar, nx), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aechdr(m), avhdr1, buf1, m0, false)), 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_read_vidhdr#(vtblpnum, apebs; avhdr; bitflips, err); wlar[vtblpnum].ec := m; if err = ESUCCESS then if avhdr = empty then if bitflips then {wlar[vtblpnum] := wl-entry(wlar[vtblpnum].ec, erasing); q := q + eq-entry(vtblpnum, none) '} else wlar[vtblpnum] := wl-entry(wlar[vtblpnum].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#(vtblpnum, 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[vtblpnum] := wl-entry(wlar[vtblpnum].ec, used); if bitflips then bflipset := bflipset ++ vtblpnum; if ladr ∈ recs then let vtblpnum0 = recs[ladr].pnum in {bflipset := bflipset -- vtblpnum0; wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, erasing); q := q + eq-entry(vtblpnum0, avhdr.vol × avhdr.leb) '}; recs[ladr] := recovery-entry(vtblpnum, avhdr.sqn)} else {wlar[vtblpnum] := wl-entry(wlar[vtblpnum].ec, erasing); q := q + eq-entry(vtblpnum, ladr.vol × ladr.leb) '}} else {wlar[vtblpnum] := wl-entry(wlar[vtblpnum].ec, erasing); q := q + eq-entry(vtblpnum, none) '}}} else {wlar[vtblpnum] := wl-entry(wlar[vtblpnum].ec, erasing); q := q + eq-entry(vtblpnum, none) '}; vtblpnum := vtblpnum + 1⟫ ( vtblpnum ≤ # apebs ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → # apebs = # wlar ∧ nx < vtblpnum ∧ indices-erasing(wlar, nx) ∧ valid-global-sqn(subarray(apebs, 0, vtblpnum), sqnum) ∧ valid-eraseq(subarray(wlar, 0, vtblpnum), q) ∧ bflipset-cons(bflipset, subarray(wlar, 0, vtblpnum)) ∧ valid-eraseq-stronger(subarray(apebs, 0, vtblpnum), q) ∧ valid-wl(subarray(apebs, 0, vtblpnum), subarray(wlar, 0, vtblpnum)) ∧ valid-recs-sqns(apebs, recs) ∧ valid-recs(subarray(apebs, 0, vtblpnum), subarray(wlar, 0, vtblpnum), recs)) ∧ # apebs < n0 + vtblpnum)

Rule argument

Additional information

Used simplifier rules: ubi-io-inv-fwd: n < # apebs ⊦ apebs[n] = apeb ∧ ubi-io-inv(apebs) → ubi-io-peb-inv(apeb);%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ aechdr(m).valid?; (s)