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Proof step 27 from proof prepost-atomic-leb-change (previous step)

# apebs = # wlar, LEB_SIZE = n2 + n0, wlar[n1] = wl-entry(m1, free), apebs[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), apebs1 = apebs, avhdr = avidhdr(v, m0, sqnum, datasize(buf, n0), 0).checksum:= checksum(buf, datasize(buf, n0)), vtblpnum = n1, aehdr.valid?, avidhdr(v, m0, sqnum, datasize(buf, n0), 0).valid?, n1 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-write-vidhdr-pre(vtblpnum, avhdr, apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum1), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum1), valid-wl(apebs, wlar), n0 ≤ # buf, n0 ≤ LEB_SIZE, v ∈ vols ∧ m0 < # vols[v] ∨ v = VTBL_VOLID ∧ m0 = VTBL_LNUM ⊦ [fail_or_success#(; ; err); if err = ESUCCESS then apebs[vtblpnum].vidhdr := avhdr else choose avhdr with ¬ avhdr.valid? in apebs[vtblpnum].vidhdr := avhdr] ( ubi-io-inv(apebs) → ⟪vtblpnum2 := n1; if err = ESUCCESS then if datasize(buf, n0) ≠ 0 then aubi_io_write_data_wl#(vtblpnum2, align↑(datasize(buf, n0), EB_PAGE_SIZE), buf; apebs; err); vtblpnum0 := vtblpnum1; vols0 := vols; q0 := q; if err = ESUCCESS then {if v = VTBL_VOLID ∧ m0 = VTBL_LNUM then {ubi_wl_put_peb#(VTBL_VOLID × VTBL_LNUM, vtblpnum0; wlar, q); bflipset := bflipset -- vtblpnum0; vtblpnum0 := vtblpnum2} else {vtblpnum3 := m0; if vols[v][vtblpnum3] ≠ unmapped then let vtblpnum0 = vols[v][vtblpnum3].pnum in {ubi_wl_put_peb#(v × vtblpnum3, vtblpnum0; wlar, q); bflipset := bflipset -- vtblpnum0}; vols[v][vtblpnum3] := ⌜vtblpnum2⌝ }; wlar[vtblpnum2] := wl-entry(wlar[vtblpnum2].ec, used)} else ubi_wl_put_peb#(none, vtblpnum2; wlar, q)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id○(apebs, apebs1, n1) ∧ ubi-io-inv(apebs) ∧ # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum + 1) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs, q) ∧ ¬ VTBL_VOLID ∈ vols ∧ bflipset-cons(bflipset, wlar) ∧ ( v ∈ vols0 ∨ is-encoded(to-vtbl(vols0), subarray(buf, 0, LEB_SIZE)) ∧ n0 = LEB_SIZE ∨ err ≠ ESUCCESS → valid-ebatbl(apebs, wlar, vols, vtblpnum0) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum0)) ∧ ( err = ESUCCESS ∧ v = VTBL_VOLID ∧ m0 = VTBL_LNUM → (∀ v0, m0. ¬ v0 ∈ vols0 ∧ is-encoded(to-vtbl(vols0)[v0, m0], subarray(buf, 0, LEB_SIZE)) ∧ n0 = LEB_SIZE → valid-ebatbl(apebs, wlar, vols[v0, fill(mkebatbl(m0), unmapped)], vtblpnum0) ∧ valid-vtbl(apebs, vols[v0, fill(mkebatbl(m0), unmapped)], wlar, vtblpnum0))) ∧ (err = ESUCCESS ∧ v ∈ vols0 ∧ vols0[v][m0] ≠ unmapped → q = q0 + eq-entry(vols0[v][m0].pnum, v × m0) ') ∧ (err = ESUCCESS ∧ v = VTBL_VOLID ∧ m0 = VTBL_LNUM → q = q0 + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ') ∧ id(apebs, apebs1, mapped-pebs(vols0)) ∧ (v = VTBL_VOLID ∧ m0 = VTBL_LNUM ∨ err ≠ ESUCCESS → vols = vols0) ∧ (v ∈ vols0 ∧ err = ESUCCESS → vols = vols0[v, vols0[v][m0, ⌜n1⌝ ]]) ∧ ( err = ESUCCESS → apebs[n1].fill = align↑(datasize(buf, n0), EB_PAGE_SIZE) ∧ apebs[n1].data = subarray(buf, 0, n0) + mkempbuf(n2) ∧ q.lebrefs ⊆ q0.lebrefs ++ (v × m0)) ∧ (err ≠ ESUCCESS → q.lebrefs = q0.lebrefs))), vtblpnum1 = n1, VTBL_VOLID ∈ vols, vtblpnum1 ∈ q, ∃ buf0. buf = mkempbuf(n0) + buf0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
# apebs = # wlar, LEB_SIZE = n2 + n0, wlar[n1] = wl-entry(m1, free), apebs[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), vtblpnum1 ≠ n1, aehdr.valid?, n1 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum1), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum1), valid-wl(apebs, wlar), n0 ≤ # buf, n0 ≤ LEB_SIZE, ¬ vtblpnum1 ∈ q, ¬ VTBL_VOLID ∈ vols, v ∈ vols ∧ m0 < # vols[v] ∨ v = VTBL_VOLID ∧ m0 = VTBL_LNUM ⊦ [fail_or_success#(; ; err); apebs1 := apebs; if err = ESUCCESS then apebs[n1].vidhdr := avidhdr(v, m0, sqnum, datasize(buf, n0), 0).checksum:= checksum(buf, datasize(buf, n0)) else {vtblpnum := n1; choose avhdr with ¬ avhdr.valid? in apebs[vtblpnum].vidhdr := avhdr}] ( ubi-io-inv(apebs) → ⟪vtblpnum2 := n1; if err = ESUCCESS then if datasize(buf, n0) ≠ 0 then aubi_io_write_data_wl#(vtblpnum2, align↑(datasize(buf, n0), EB_PAGE_SIZE), buf; apebs; err); vtblpnum0 := vtblpnum1; vols0 := vols; q0 := q; if err = ESUCCESS then {if v = VTBL_VOLID ∧ m0 = VTBL_LNUM then {ubi_wl_put_peb#(VTBL_VOLID × VTBL_LNUM, vtblpnum0; wlar, q); bflipset := bflipset -- vtblpnum0; vtblpnum0 := vtblpnum2} else {vtblpnum3 := m0; if vols[v][vtblpnum3] ≠ unmapped then let vtblpnum0 = vols[v][vtblpnum3].pnum in {ubi_wl_put_peb#(v × vtblpnum3, vtblpnum0; wlar, q); bflipset := bflipset -- vtblpnum0}; vols[v][vtblpnum3] := ⌜vtblpnum2⌝ }; wlar[vtblpnum2] := wl-entry(wlar[vtblpnum2].ec, used)} else ubi_wl_put_peb#(none, vtblpnum2; wlar, q)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id○(apebs, apebs1, n1) ∧ ubi-io-inv(apebs) ∧ # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum + 1) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs, q) ∧ ¬ VTBL_VOLID ∈ vols ∧ bflipset-cons(bflipset, wlar) ∧ ( v ∈ vols0 ∨ is-encoded(to-vtbl(vols0), subarray(buf, 0, LEB_SIZE)) ∧ n0 = LEB_SIZE ∨ err ≠ ESUCCESS → valid-ebatbl(apebs, wlar, vols, vtblpnum0) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum0)) ∧ ( err = ESUCCESS ∧ v = VTBL_VOLID ∧ m0 = VTBL_LNUM → (∀ v0, m0. ¬ v0 ∈ vols0 ∧ is-encoded(to-vtbl(vols0)[v0, m0], subarray(buf, 0, LEB_SIZE)) ∧ n0 = LEB_SIZE → valid-ebatbl(apebs, wlar, vols[v0, fill(mkebatbl(m0), unmapped)], vtblpnum0) ∧ valid-vtbl(apebs, vols[v0, fill(mkebatbl(m0), unmapped)], wlar, vtblpnum0))) ∧ (err = ESUCCESS ∧ v ∈ vols0 ∧ vols0[v][m0] ≠ unmapped → q = q0 + eq-entry(vols0[v][m0].pnum, v × m0) ') ∧ (err = ESUCCESS ∧ v = VTBL_VOLID ∧ m0 = VTBL_LNUM → q = q0 + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ') ∧ id(apebs, apebs1, mapped-pebs(vols0)) ∧ (v = VTBL_VOLID ∧ m0 = VTBL_LNUM ∨ err ≠ ESUCCESS → vols = vols0) ∧ (v ∈ vols0 ∧ err = ESUCCESS → vols = vols0[v, vols0[v][m0, ⌜n1⌝ ]]) ∧ ( err = ESUCCESS → apebs[n1].fill = align↑(datasize(buf, n0), EB_PAGE_SIZE) ∧ apebs[n1].data = subarray(buf, 0, n0) + mkempbuf(n2) ∧ q.lebrefs ⊆ q0.lebrefs ++ (v × m0)) ∧ (err ≠ ESUCCESS → q.lebrefs = q0.lebrefs))), ∃ buf0. buf = mkempbuf(n0) + buf0

Rule argument

Additional information

Used simplifier rules: lf-valid-vtbl-neq-free: ⊦ wlar[m] = wl-entry(m0, free) ∧ valid-vtbl(apebs, vols, wlar, n) → n ≠ m;%lf-vtbl-info: ⊦ valid-vtbl(apebs, vols, wlar, n) ∧ valid-eraseq(wlar, q) → ¬ n ∈ q;% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ avidhdr(v, m, m0, m1, m2).valid?; (s)%⊦ ubi-io-write-vidhdr-pre(n, avhdr, apebs) ↔ n < # apebs ∧ ¬ apebs[n].bad ∧ avhdr.valid? ∧ apebs[n].echdr.valid? ∧ apebs[n].vidhdr = empty; (s)% ⊦ avidhdr(v, m, m0, m1, m2).checksum:= m6 = avidhdr(v, m, m0, m1, m6); (s)