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Proof step 36 from proof delta-atomic-leb-change (previous step)

apebs0[n2] = mkpeb(aehdr, empty, buf1, m, false), wlar[n2] = wl-entry(m0, stat), wlar[n1] = wl-entry(m1, stat0), apebs = apebs0[n2, mkpeb(aehdr, avidhdr(v, m2, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), buf1, m, false)], buf0 = buf, n = align↑(datasize(buf, n0), EB_PAGE_SIZE), vtblpnum = n2, aehdr.valid?, n2 < # apebs0, n2 < # wlar, n1 < # wlar, ubi-io-write-data-wl-pre(vtblpnum, n, buf0, apebs), v ∈ vols ∧ m2 < # vols[v] ∧ vols[v][m2] = ⌜n1⌝ ∨ v = VTBL_VOLID ∧ m2 = VTBL_LNUM ∧ vtblpnum1 = n1 ⊦ [fail_or_success#(; ; err); if err = ESUCCESS then apebs[vtblpnum] := mkpeb(apebs[vtblpnum].echdr, apebs[vtblpnum].vidhdr, subarray(buf0, 0, n) + mkempbuf(LEB_SIZE - n), n, apebs[vtblpnum].bad) else choose buf with # buf ≤ n ∧ is-aligned(# buf, EB_PAGE_SIZE) ∧ ( datasize(buf, # buf) < datasize(buf0, n) ∨ checksum(buf + mkempbuf(n - # buf), datasize(buf0, n)) ≠ checksum(buf0, datasize(buf0, n))) in apebs[vtblpnum] := mkpeb(apebs[vtblpnum].echdr, apebs[vtblpnum].vidhdr, buf + mkempbuf(LEB_SIZE - # buf), # buf, apebs[vtblpnum].bad); wlar0 := wlar; err0 := err; if err0 = ESUCCESS then {vtblpnum2 := n2; if v = VTBL_VOLID ∧ m2 = VTBL_LNUM then {ubi_wl_put_peb#(VTBL_VOLID × VTBL_LNUM, vtblpnum1; wlar, q); bflipset := bflipset -- vtblpnum1; vtblpnum1 := vtblpnum2} else {if vols[v][m2] ≠ unmapped then let vtblpnum0 = vols[v][m2].pnum in {ubi_wl_put_peb#(v × m2, vtblpnum0; wlar, q); bflipset := bflipset -- vtblpnum0}; vols[v][m2] := ⌜vtblpnum2⌝ }; wlar[vtblpnum2] := wl-entry(wlar[vtblpnum2].ec, used)} else ubi_wl_put_peb#(none, n2; wlar, q)] ( sum-of-differences(ecs(wlar).max, ecs(wlar)) = sum-of-differences(ecs(wlar0).max, ecs(wlar0)) ∧ ecs(wlar) = ecs(wlar0) ∧ (err0 = ESUCCESS → wlar[n2].ec = m0 ∧ wlar[n1].ec = m1)), datasize(buf, n0) = 0, n2 = n1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
apebs0[n2] = mkpeb(aehdr, empty, buf1, 0, false), wlar[n2] = wl-entry(m0, stat), wlar[n1] = wl-entry(m1, stat0), align↑(datasize(buf, n0), EB_PAGE_SIZE) = align↑(datasize(buf, align↑(datasize(buf, n0), EB_PAGE_SIZE)), EB_PAGE_SIZE), datasize(buf, align↑(datasize(buf, n0), EB_PAGE_SIZE)) ≠ 0, datasize(buf, n0) ≠ 0, n2 ≠ n1, aehdr.valid?, n2 < # apebs0, n2 < # wlar, n1 < # wlar, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ # buf, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ LEB_SIZE, v ∈ vols ∧ m2 < # vols[v] ∧ vols[v][m2] = ⌜n1⌝ ∨ v = VTBL_VOLID ∧ m2 = VTBL_LNUM ∧ vtblpnum1 = n1 ⊦ [fail_or_success#(; ; err); if err = ESUCCESS then apebs := apebs0[n2, mkpeb(aehdr, avidhdr(v, m2, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), buf1, 0, false)] [n2, mkpeb (apebs0[n2, mkpeb(aehdr, avidhdr(v, m2, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), buf1, 0, false)][n2].echdr, apebs0[n2, mkpeb(aehdr, avidhdr(v, m2, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), buf1, 0, false)][n2].vidhdr, subarray(buf, 0, align↑(datasize(buf, n0), EB_PAGE_SIZE)) + mkempbuf(LEB_SIZE - align↑(datasize(buf, n0), EB_PAGE_SIZE)), align↑(datasize(buf, n0), EB_PAGE_SIZE), apebs0[n2, mkpeb(aehdr, avidhdr(v, m2, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), buf1, 0, false)][n2].bad) ] else {vtblpnum := n2; n := align↑(datasize(buf, n0), EB_PAGE_SIZE); buf0 := buf; apebs := apebs0[n2, mkpeb(aehdr, avidhdr(v, m2, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), buf1, 0, false)]; choose buf2 with # buf2 ≤ n ∧ is-aligned(# buf2, EB_PAGE_SIZE) ∧ ( datasize(buf2, # buf2) < datasize(buf0, n) ∨ checksum(buf2 + mkempbuf(n - # buf2), datasize(buf0, n)) ≠ checksum(buf0, datasize(buf0, n))) in apebs[vtblpnum] := mkpeb(apebs[vtblpnum].echdr, apebs[vtblpnum].vidhdr, buf2 + mkempbuf(LEB_SIZE - # buf2), # buf2, apebs[vtblpnum].bad)}; wlar0 := wlar; err0 := err; if err0 = ESUCCESS then {vtblpnum2 := n2; if v = VTBL_VOLID ∧ m2 = VTBL_LNUM then {ubi_wl_put_peb#(VTBL_VOLID × VTBL_LNUM, vtblpnum1; wlar, q); bflipset := bflipset -- vtblpnum1; vtblpnum1 := vtblpnum2} else {if vols[v][m2] ≠ unmapped then let vtblpnum0 = vols[v][m2].pnum in {ubi_wl_put_peb#(v × m2, vtblpnum0; wlar, q); bflipset := bflipset -- vtblpnum0}; vols[v][m2] := ⌜vtblpnum2⌝ }; wlar[vtblpnum2] := wl-entry(wlar[vtblpnum2].ec, used)} else ubi_wl_put_peb#(none, n2; wlar, q)] ( sum-of-differences(ecs(wlar).max, ecs(wlar)) = sum-of-differences(ecs(wlar0).max, ecs(wlar0)) ∧ ecs(wlar) = ecs(wlar0) ∧ (err0 = ESUCCESS → wlar[n2].ec = m0 ∧ wlar[n1].ec = m1))

Rule argument

Additional information

Used simplifier rules: ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).fill = m; (s)% ⊦ avidhdr(v, m, m0, m1, m2).valid?; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ m < # apebs → apebs[m, apeb][m] = apeb; (s)% ⊦ # apebs[n, apeb] = # apebs; (s)%⊦ ubi-io-write-data-wl-pre(n, n1, buf, apebs) ↔ n < # apebs ∧ ¬ apebs[n].bad ∧ apebs[n].echdr.valid? ∧ apebs[n].vidhdr.valid? ∧ n1 = align↑(datasize(buf, n1), EB_PAGE_SIZE) ∧ apebs[n].fill = 0 ∧ n1 ≤ LEB_SIZE ∧ n1 ≤ # buf ∧ datasize(buf, n1) ≠ 0; (s)