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Proof step 23 from proof delta-atomic-leb-change (previous step)

apebs[n2].vidhdr = empty, wlar[n2] = wl-entry(m0, stat), wlar[n1] = wl-entry(m1, stat0), datasize(buf, n) ≠ 0, n2 ≠ n1, apebs[n2].echdr.valid?, n2 < # apebs, n2 < # wlar, n1 < # wlar, ¬ apebs[n2].bad, 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[n2].vidhdr := avidhdr(v, m2, sqnum, datasize(buf, n), 0).checksum:= checksum(buf, datasize(buf, n)) else {vtblpnum := n2; choose avhdr with ¬ avhdr.valid? in apebs[vtblpnum].vidhdr := avhdr}; vtblpnum2 := n2; if err = ESUCCESS then if datasize(buf, n) ≠ 0 then aubi_io_write_data_wl#(vtblpnum2, align↑(datasize(buf, n), EB_PAGE_SIZE), buf; apebs; err); wlar0 := wlar; if err = ESUCCESS then {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, vtblpnum2; wlar, q)] ( sum-of-differences(ecs(wlar).max, ecs(wlar)) = sum-of-differences(ecs(wlar0).max, ecs(wlar0)) ∧ ecs(wlar) = ecs(wlar0) ∧ (err = ESUCCESS → wlar[n2].ec = m0 ∧ wlar[n1].ec = m1))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 24:
wlar[n1] = wl-entry(m1, stat0), wlar[n2] = wl-entry(m0, stat), apebs[n2] = mkpeb(aehdr, avhdr0, buf0, m, boolvar), avhdr0 = empty, ¬ boolvar, aehdr.valid?, n1 < # wlar, n2 < # wlar, n2 < # 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[n2].vidhdr := avidhdr(v, m2, sqnum, datasize(buf, n), 0).checksum:= checksum(buf, datasize(buf, n)) else {vtblpnum := n2; choose avhdr with ¬ avhdr.valid? in apebs[vtblpnum].vidhdr := avhdr}; vtblpnum2 := n2; if err = ESUCCESS then if datasize(buf, n) ≠ 0 then aubi_io_write_data_wl#(vtblpnum2, align↑(datasize(buf, n), EB_PAGE_SIZE), buf; apebs; err); wlar0 := wlar; if err = ESUCCESS then {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, vtblpnum2; wlar, q)] ( sum-of-differences(ecs(wlar).max, ecs(wlar)) = sum-of-differences(ecs(wlar0).max, ecs(wlar0)) ∧ ecs(wlar) = ecs(wlar0) ∧ (err = ESUCCESS → wlar[n2].ec = m0 ∧ wlar[n1].ec = m1)), datasize(buf, n) = 0, n2 = n1

Rule argument

spec: apeb name: elim seq: ⊦ ( ( (aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar) subst: [apeb, aehdr, avhdr, buf, m, boolvar] → [apebs[n2], aehdr, avhdr0, buf0, m, boolvar]

Additional information

Used simplifier rules: ⊦ ( ((aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar); (elim) Used terms: apebs[n2], aehdr, avhdr0, buf0, m, boolvar