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Proof step 114 from proof prepost-scan-all (previous step)

# wlar0 = n1 + vtblpnum1, # apebs = n1 + vtblpnum1, apebs[vtblpnum1] = mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, m4), buf1, m0, false), buf = mkbuf(LEB_SIZE), buf0 = buf, n = LEB_SIZE, n0 = 0, vtblpnum = 0, vtblpnum0 = vtblpnum1, nx < vtblpnum1, bflipset-cons(bflipset, subarray(wlar0, 0, vtblpnum1)), indices-erasing(wlar0, nx), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, m4), buf1, m0, false)), ubi-io-read-data-pre(vtblpnum0, vtblpnum, n0, n, buf0, apebs), unique-sqns(apebs), valid-eraseq(subarray(wlar0, 0, vtblpnum1), q), valid-eraseq-stronger(subarray(apebs, 0, vtblpnum1), q), valid-global-sqn(subarray(apebs, 0, vtblpnum1), sqnum), valid-recs(subarray(apebs, 0, vtblpnum1), subarray(wlar0, 0, vtblpnum1), recs), valid-recs-sqns(apebs, recs), valid-wl(subarray(apebs, 0, vtblpnum1), subarray(wlar0, 0, vtblpnum1)) ⊦ ⟪fail_or_success#(; ; err); bitflips := ?; if err = ESUCCESS then buf0 := copy(apebs[vtblpnum0].data, vtblpnum, buf0, n0, n) else choose buf with # buf = # buf0 ∧ range=(buf, 0, buf0, 0, n0) ∧ range=(buf, n0 + n, buf0, n0 + n, # buf0 - n0 + n) in buf0 := buf; bitflips0 := bitflips0 ∨ bitflips; wlar := wlar0[vtblpnum1, wlar0[vtblpnum1].ec:= m]; if err = ESUCCESS then let ladr = apebs[vtblpnum1].vidhdr.vol × apebs[vtblpnum1].vidhdr.leb, n = 0 in {if ladr ∈ recs then n := recs[ladr].sqn; if apebs[vtblpnum1].vidhdr.size ≠ 0 → apebs[vtblpnum1].vidhdr.size ≤ datasize(buf0) ∧ apebs[vtblpnum1].vidhdr.checksum = checksum(buf0, apebs[vtblpnum1].vidhdr.size) then {sqnum := max(sqnum, apebs[vtblpnum1].vidhdr.sqn + 1); if n ≤ apebs[vtblpnum1].vidhdr.sqn then {wlar[vtblpnum1] := wl-entry(wlar[vtblpnum1].ec, used); if bitflips0 then bflipset := bflipset ++ vtblpnum1; avhdr := apebs[vtblpnum1].vidhdr; 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(vtblpnum1, avhdr.sqn)} else {wlar[vtblpnum1] := wl-entry(wlar[vtblpnum1].ec, erasing); q := q + eq-entry(vtblpnum1, ladr.vol × ladr.leb) '}} else {wlar[vtblpnum1] := wl-entry(wlar[vtblpnum1].ec, erasing); q := q + eq-entry(vtblpnum1, none) '}}; vtblpnum1 := vtblpnum1 + 1⟫ ( vtblpnum1 ≤ # apebs ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → # apebs = # wlar ∧ nx < vtblpnum1 ∧ indices-erasing(wlar, nx) ∧ valid-global-sqn(subarray(apebs, 0, vtblpnum1), sqnum) ∧ valid-eraseq(subarray(wlar, 0, vtblpnum1), q) ∧ bflipset-cons(bflipset, subarray(wlar, 0, vtblpnum1)) ∧ valid-eraseq-stronger(subarray(apebs, 0, vtblpnum1), q) ∧ valid-wl(subarray(apebs, 0, vtblpnum1), subarray(wlar, 0, vtblpnum1)) ∧ valid-recs-sqns(apebs, recs) ∧ valid-recs(subarray(apebs, 0, vtblpnum1), subarray(wlar, 0, vtblpnum1), recs)) ∧ # apebs < n1 + vtblpnum1), m3 = 0, n1 = 0, dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 115:
# apebs = n1 + vtblpnum1, # wlar0 = n1 + vtblpnum1, apebs[vtblpnum1] = mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, m4), buf1, m0, false), m3 ≠ 0, n1 ≠ 0, nx < vtblpnum1, bflipset-cons(bflipset, subarray(wlar0, 0, vtblpnum1)), indices-erasing(wlar0, nx), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, m4), buf1, m0, false)), unique-sqns(apebs), valid-eraseq(subarray(wlar0, 0, vtblpnum1), q), valid-eraseq-stronger(subarray(apebs, 0, vtblpnum1), q), valid-global-sqn(subarray(apebs, 0, vtblpnum1), sqnum), valid-recs(subarray(apebs, 0, vtblpnum1), subarray(wlar0, 0, vtblpnum1), recs), valid-recs-sqns(apebs, recs), valid-wl(subarray(apebs, 0, vtblpnum1), subarray(wlar0, 0, vtblpnum1)), ¬ dups(nx) ⊦ ⟪fail_or_success#(; ; err); bitflips := ?; buf := mkbuf(LEB_SIZE); if err = ESUCCESS then buf := copy(apebs[vtblpnum1].data, 0, buf, 0, LEB_SIZE) else {n0 := 0; n := LEB_SIZE; choose buf1 with # buf1 = # buf ∧ range=(buf1, 0, buf, 0, n0) ∧ range=(buf1, n0 + n, buf, n0 + n, # buf - n0 + n) in buf := buf1}; bitflips0 := bitflips0 ∨ bitflips; wlar := wlar0[vtblpnum1, wlar0[vtblpnum1].ec:= m]; if err = ESUCCESS then let ladr = apebs[vtblpnum1].vidhdr.vol × apebs[vtblpnum1].vidhdr.leb, n = 0 in {if ladr ∈ recs then n := recs[ladr].sqn; if apebs[vtblpnum1].vidhdr.size ≠ 0 → apebs[vtblpnum1].vidhdr.size ≤ datasize(buf) ∧ apebs[vtblpnum1].vidhdr.checksum = checksum(buf, apebs[vtblpnum1].vidhdr.size) then {sqnum := max(sqnum, apebs[vtblpnum1].vidhdr.sqn + 1); if n ≤ apebs[vtblpnum1].vidhdr.sqn then {wlar[vtblpnum1] := wl-entry(wlar[vtblpnum1].ec, used); if bitflips0 then bflipset := bflipset ++ vtblpnum1; avhdr := apebs[vtblpnum1].vidhdr; 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(vtblpnum1, avhdr.sqn)} else {wlar[vtblpnum1] := wl-entry(wlar[vtblpnum1].ec, erasing); q := q + eq-entry(vtblpnum1, ladr.vol × ladr.leb) '}} else {wlar[vtblpnum1] := wl-entry(wlar[vtblpnum1].ec, erasing); q := q + eq-entry(vtblpnum1, none) '}}; vtblpnum1 := vtblpnum1 + 1⟫ ( vtblpnum1 ≤ # apebs ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → # apebs = # wlar ∧ nx < vtblpnum1 ∧ indices-erasing(wlar, nx) ∧ valid-global-sqn(subarray(apebs, 0, vtblpnum1), sqnum) ∧ valid-eraseq(subarray(wlar, 0, vtblpnum1), q) ∧ bflipset-cons(bflipset, subarray(wlar, 0, vtblpnum1)) ∧ valid-eraseq-stronger(subarray(apebs, 0, vtblpnum1), q) ∧ valid-wl(subarray(apebs, 0, vtblpnum1), subarray(wlar, 0, vtblpnum1)) ∧ valid-recs-sqns(apebs, recs) ∧ valid-recs(subarray(apebs, 0, vtblpnum1), subarray(wlar, 0, vtblpnum1), recs)) ∧ # apebs < n1 + vtblpnum1)

Rule argument

Additional information

Used simplifier rules: ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ 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% ⊦ # mkbuf(n) = n; (s)% ⊦ m ≤ m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)%⊦ ubi-io-read-data-pre(n, n0, m0, n1, buf, apebs) ↔ n < # apebs ∧ ¬ apebs[n].bad ∧ n0 + n1 ≤ LEB_SIZE ∧ m0 + n1 ≤ # buf; (s)