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Proof step 43 from proof prepost-atomic-leb-change (previous step)

# apebs0 = # wlar, LEB_SIZE = n2 + n0, wlar[n1] = wl-entry(m1, free), apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), apebs = apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), mkempbuf(LEB_SIZE), 0, false)], vtblpnum1 ≠ n1, aehdr.valid?, n1 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), mkempbuf(LEB_SIZE), 0, false)]), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), n0 ≤ # buf, n0 ≤ LEB_SIZE, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ LEB_SIZE, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ # buf, ¬ vtblpnum1 ∈ q, ¬ VTBL_VOLID ∈ vols, v ∈ vols ∧ m0 < # vols[v] ∨ v = VTBL_VOLID ∧ m0 = VTBL_LNUM ⊦ [aubi_io_write_data_wl#(n1, align↑(datasize(buf, n0), EB_PAGE_SIZE), buf; apebs; err0)] ( ubi-io-inv(apebs) → ⟪vtblpnum0 := vtblpnum1; vols0 := vols; q0 := q; if err0 = ESUCCESS then {vtblpnum2 := n1; 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, n1; wlar, q)⟫ ( (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ id○(apebs, apebs0, n1) ∧ # 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 ∨ err0 ≠ ESUCCESS → valid-ebatbl(apebs, wlar, vols, vtblpnum0) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum0)) ∧ ( err0 = 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))) ∧ (err0 = ESUCCESS ∧ v ∈ vols0 ∧ vols0[v][m0] ≠ unmapped → q = q0 + eq-entry(vols0[v][m0].pnum, v × m0) ') ∧ (err0 = ESUCCESS ∧ v = VTBL_VOLID ∧ m0 = VTBL_LNUM → q = q0 + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ') ∧ id(apebs, apebs0, mapped-pebs(vols0)) ∧ (v = VTBL_VOLID ∧ m0 = VTBL_LNUM ∨ err0 ≠ ESUCCESS → vols = vols0) ∧ (v ∈ vols0 ∧ err0 = ESUCCESS → vols = vols0[v, vols0[v][m0, ⌜n1⌝ ]]) ∧ ( err0 = 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)) ∧ (err0 ≠ ESUCCESS → q.lebrefs = q0.lebrefs))), ∃ buf0. buf = mkempbuf(n0) + buf0

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 44:
# apebs0 = # wlar, LEB_SIZE = n2 + n0, apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar[n1] = wl-entry(m1, free), apebs = apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), mkempbuf(LEB_SIZE), 0, false)], buf0 = buf, n = align↑(datasize(buf, n0), EB_PAGE_SIZE), vtblpnum = n1, aehdr.valid?, n1 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), mkempbuf(LEB_SIZE), 0, false)]), ubi-io-inv(apebs0), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ # buf, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ LEB_SIZE, n0 ≤ LEB_SIZE, n0 ≤ # buf, v ∈ vols ∧ m0 < # vols[v] ∨ v = VTBL_VOLID ∧ m0 = VTBL_LNUM ⊦ [if ubi-io-write-data-wl-pre(vtblpnum, n, buf0, apebs) then {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)} else abort] ( ubi-io-inv(apebs) → ⟪vtblpnum0 := vtblpnum1; vols0 := vols; q0 := q; err0 := err; if err0 = ESUCCESS then {vtblpnum2 := n1; 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, n1; wlar, q)⟫ ( (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ id○(apebs, apebs0, n1) ∧ # 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 ∨ err0 ≠ ESUCCESS → valid-ebatbl(apebs, wlar, vols, vtblpnum0) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum0)) ∧ ( err0 = 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))) ∧ (err0 = ESUCCESS ∧ v ∈ vols0 ∧ vols0[v][m0] ≠ unmapped → q = q0 + eq-entry(vols0[v][m0].pnum, v × m0) ') ∧ (err0 = ESUCCESS ∧ v = VTBL_VOLID ∧ m0 = VTBL_LNUM → q = q0 + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ') ∧ id(apebs, apebs0, mapped-pebs(vols0)) ∧ (v = VTBL_VOLID ∧ m0 = VTBL_LNUM ∨ err0 ≠ ESUCCESS → vols = vols0) ∧ (v ∈ vols0 ∧ err0 = ESUCCESS → vols = vols0[v, vols0[v][m0, ⌜n1⌝ ]]) ∧ ( err0 = 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)) ∧ (err0 ≠ ESUCCESS → q.lebrefs = q0.lebrefs))), vtblpnum1 = n1, vtblpnum1 ∈ q, VTBL_VOLID ∈ vols, ∃ buf0. buf = mkempbuf(n0) + buf0

Rule argument

pos: right 1

Additional information

Used simplifier rules: aubi_io_write_data_wl#(PNUM, N, BUF; APEBS; ERR) {if ubi-io-write-data-wl-pre(PNUM, N, BUF, APEBS) then {fail_or_success#(; ; ERR); if ERR = ESUCCESS then APEBS[PNUM] := mkpeb (APEBS[PNUM].echdr, APEBS[PNUM].vidhdr, subarray(BUF, 0, N) + mkempbuf(LEB_SIZE - N), N, APEBS[PNUM].bad) else choose BUF0 with # BUF0 ≤ N ∧ is-aligned(# BUF0, EB_PAGE_SIZE) ∧ ( datasize(BUF0, # BUF0) < datasize(BUF, N) ∨ checksum (BUF0 + mkempbuf(N - # BUF0), datasize(BUF, N)) ≠ checksum(BUF, datasize(BUF, N))) in APEBS[PNUM] := mkpeb (APEBS[PNUM].echdr, APEBS[PNUM].vidhdr, BUF0 + mkempbuf(LEB_SIZE - # BUF0), # BUF0, APEBS[PNUM].bad)} else abort };