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Proof step 7 from proof prepost-atomic-leb-change (previous step)

# apebs = # wlar, wlar[n] = wl-entry(m1, free), apebs[n] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), apebs0 = apebs, q0 = q, vols0 = vols, vtblpnum0 = vtblpnum, vtblpnum ≠ n, aehdr.valid?, n < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-wl(apebs, wlar), n0 ≤ # buf, n0 ≤ LEB_SIZE, ¬ VTBL_VOLID ∈ vols, ¬ vtblpnum ∈ q, v ∈ vols ∧ m < # vols[v] ∨ v = VTBL_VOLID ∧ m = VTBL_LNUM ⊦ ⟪ubi_atomic_leb_change#(v, m, n, n0, buf, EB_PAGE_SIZE; vols, wlar, q, bflipset, vtblpnum, sqnum, apebs; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id○(apebs, apebs0, n) ∧ ubi-io-inv(apebs) ∧ # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ 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, vtblpnum) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum)) ∧ ( err = ESUCCESS ∧ v = VTBL_VOLID ∧ m = 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)], vtblpnum) ∧ valid-vtbl(apebs, vols[v0, fill(mkebatbl(m0), unmapped)], wlar, vtblpnum))) ∧ (err = ESUCCESS ∧ v ∈ vols0 ∧ vols0[v][m] ≠ unmapped → q = q0 + eq-entry(vols0[v][m].pnum, v × m) ') ∧ (err = ESUCCESS ∧ v = VTBL_VOLID ∧ m = VTBL_LNUM → q = q0 + eq-entry(vtblpnum0, VTBL_VOLID × VTBL_LNUM) ') ∧ id(apebs, apebs0, mapped-pebs(vols0)) ∧ (v = VTBL_VOLID ∧ m = VTBL_LNUM ∨ err ≠ ESUCCESS → vols = vols0) ∧ (v ∈ vols0 ∧ err = ESUCCESS → vols = vols0[v, vols0[v][m, ⌜n⌝ ]]) ∧ ( err = ESUCCESS → apebs[n].fill = align↑(datasize(buf, n0), EB_PAGE_SIZE) ∧ apebs[n].data = subarray(buf, 0, n0) + mkempbuf(LEB_SIZE - n0) ∧ q.lebrefs ⊆ q0.lebrefs ++ (v × m)) ∧ (err ≠ ESUCCESS → q.lebrefs = q0.lebrefs))

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 8:
# apebs = # wlar, apebs[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar[n1] = wl-entry(m1, free), apebs0 = apebs, n = n0, q0 = q, vols0 = vols, vtblpnum0 = vtblpnum, vtblpnum1 = EB_PAGE_SIZE, vtblpnum2 = n1, vtblpnum3 = m, vtblpnum4 = vtblpnum, 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, vtblpnum), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-wl(apebs, wlar), n0 ≤ LEB_SIZE, n0 ≤ # buf, v ∈ vols ∧ m < # vols[v] ∨ v = VTBL_VOLID ∧ m = VTBL_LNUM ⊦ ⟪err := ESUCCESS; n := datasize(buf, n); let m = ? in {ubi_next_sqnum#(; sqnum; m); let avhdr = avidhdr(v, vtblpnum3, m, n, 0) in {if n ≠ 0 then avhdr.checksum := checksum(buf, n); aubi_io_write_vidhdr#(vtblpnum2, avhdr; apebs; err); if err = ESUCCESS then if n > 0 then aubi_io_write_data_wl#(vtblpnum2, align↑(n, vtblpnum1), buf; apebs; err); if err = ESUCCESS then {if v = VTBL_VOLID ∧ vtblpnum3 = VTBL_LNUM then {ubi_wl_put_peb#(VTBL_VOLID × VTBL_LNUM, vtblpnum0; wlar, q); bflipset := bflipset -- vtblpnum0; vtblpnum0 := vtblpnum2} else {if vols[v][vtblpnum3] ≠ unmapped then let vtblpnum = vols[v][vtblpnum3].pnum in {ubi_wl_put_peb#(v × vtblpnum3, vtblpnum; wlar, q); bflipset := bflipset -- vtblpnum}; vols[v][vtblpnum3] := ⌜vtblpnum2⌝ }; wlar[vtblpnum2].status := used} else ubi_wl_put_peb#(none, vtblpnum2; wlar, q)}}⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id○(apebs, apebs0, n1) ∧ ubi-io-inv(apebs) ∧ # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ 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 ∧ m = 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][m] ≠ unmapped → q = q0 + eq-entry(vols0[v][m].pnum, v × m) ') ∧ (err = ESUCCESS ∧ v = VTBL_VOLID ∧ m = VTBL_LNUM → q = q0 + eq-entry(vtblpnum4, VTBL_VOLID × VTBL_LNUM) ') ∧ id(apebs, apebs0, mapped-pebs(vols0)) ∧ (v = VTBL_VOLID ∧ m = VTBL_LNUM ∨ err ≠ ESUCCESS → vols = vols0) ∧ (v ∈ vols0 ∧ err = ESUCCESS → vols = vols0[v, vols0[v][m, ⌜n1⌝ ]]) ∧ ( err = ESUCCESS → apebs[n1].fill = align↑(datasize(buf, n0), EB_PAGE_SIZE) ∧ apebs[n1].data = subarray(buf, 0, n0) + mkempbuf(LEB_SIZE - n0) ∧ q.lebrefs ⊆ q0.lebrefs ++ (v × m)) ∧ (err ≠ ESUCCESS → q.lebrefs = q0.lebrefs)), vtblpnum = n1, VTBL_VOLID ∈ vols, vtblpnum ∈ q

Rule argument

pos: right 1

Additional information

Used simplifier rules: atomic-leb-change: ⊦ ;