[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 10 from proof inv-create-volume (previous step)

# apebs = # wlar, apebs0 = apebs, q0 = q, v ≠ VTBL_VOLID, bflipset-cons(bflipset, wlar), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum3), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum3), valid-wl(apebs, wlar), 2 * ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vols + ENCODED_VOLID_SIZE ≤ LEB_SIZE, ¬ v ∈ vols, ¬ VTBL_VOLID ∈ vols, ¬ vtblpnum3 ∈ q ⊦ ⟪ubi_erase_all#(vols, bflipset, vtblpnum3, sqnum; wlar, q, apebs; err); vols0 := vols; if err = ESUCCESS then {ubi_wl_get_peb#(; vtblpnum, wlar, q, apebs; err); if err = ESUCCESS then let vtbl = to-vtbl(vols) in {vtbl[v] := n; let buf = mkbuf(LEB_SIZE), vtbl = to-vtbl(vols) in {vtbl[v] := n; encode_vtbl#(; vtbl, buf; err); if err = ESUCCESS then {ubi_atomic_leb_change# (VTBL_VOLID, VTBL_LNUM, vtblpnum, LEB_SIZE, buf, EB_PAGE_SIZE; vols, wlar, q, bflipset, vtblpnum3, sqnum, apebs; err); if err = ESUCCESS then {vols[v] := mkebatbl(n); vols[v] := fill(vols[v], unmapped)}}}}}⟫ ( # 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) ∧ valid-ebatbl(apebs, wlar, vols, vtblpnum3) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum3) ∧ ubi-io-inv(apebs) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id(apebs, apebs0, mapped-pebs(vols)) ∧ (err = ESUCCESS → ¬ v ∈ vols0 ∧ vols = vols0[v, fill(mkebatbl(n), unmapped)] ∧ q.lebrefs ⊆ ∅ ++ (VTBL_VOLID × VTBL_LNUM)) ∧ (err ≠ ESUCCESS → q.lebrefs ⊆ q0.lebrefs ∧ vols = vols0))

User applied rule insert program lemma

And obtained the following new goals

Proof step 11:
ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum), ubi-io-inv(apebs), apebs0 = apebs, q0 = q ⊦ ⟪ubi_erase_all#(vols, bflipset, vtblpnum, sqnum; wlar, q, apebs; err)⟫ ( ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum) ∧ ubi-io-inv(apebs) ∧ id(apebs, apebs0, mapped-pebs(vols)) ∧ q ⊆ q0 ∧ (err = ESUCCESS → q = []) ∧ (err = ESUCCESS ∨ ⌊err⌋ ))
Proof step 12:
# apebs = # wlar, apebs = apebs, apebs0 = apebs, apebs1 = apebs, bflipset0 = bflipset, q = q, q0 = q, q1 = q, sqnum0 = sqnum, vols1 = vols, vtblpnum0 = vtblpnum3, bflipset-cons(bflipset, wlar), ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum3, sqnum), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum3), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum3), valid-wl(apebs, wlar), 2 * ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vols + ENCODED_VOLID_SIZE ≤ LEB_SIZE ⊦ [ubi_erase_all#(vols, bflipset, vtblpnum3, sqnum; wlar, q, apebs; err)] ( ubi-cons(apebs, vols1, wlar, q, bflipset0, vtblpnum0, sqnum0) ∧ ubi-io-inv(apebs) ∧ id(apebs, apebs1, mapped-pebs(vols1)) ∧ q ⊆ q1 ∧ (err = ESUCCESS → q = []) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) → ⟪vols0 := vols; if err = ESUCCESS then {ubi_wl_get_peb#(; vtblpnum, wlar, q, apebs; err); if err = ESUCCESS then let vtbl = to-vtbl(vols) in {vtbl[v] := n; let buf = mkbuf(LEB_SIZE), vtbl = to-vtbl(vols) in {vtbl[v] := n; encode_vtbl#(; vtbl, buf; err); if err = ESUCCESS then {ubi_atomic_leb_change# (VTBL_VOLID, VTBL_LNUM, vtblpnum, LEB_SIZE, buf, EB_PAGE_SIZE; vols, wlar, q, bflipset, vtblpnum3, sqnum, apebs; err); if err = ESUCCESS then {vols[v] := mkebatbl(n); vols[v] := fill(vols[v], unmapped)}}}}}⟫ ( # 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) ∧ valid-ebatbl(apebs, wlar, vols, vtblpnum3) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum3) ∧ ubi-io-inv(apebs) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id(apebs, apebs0, mapped-pebs(vols)) ∧ (err = ESUCCESS → ¬ v ∈ vols0 ∧ vols = vols0[v, fill(mkebatbl(n), unmapped)] ∧ q.lebrefs ⊆ ∅ ++ (VTBL_VOLID × VTBL_LNUM)) ∧ (err ≠ ESUCCESS → q.lebrefs ⊆ q0.lebrefs ∧ vols = vols0))), v = VTBL_VOLID, v ∈ vols, VTBL_VOLID ∈ vols, vtblpnum3 ∈ q

Rule argument

spec: <toplevel> name: inv-erase-all seq: ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum), ubi-io-inv(apebs), apebs0 = apebs, q0 = q ⊦ ⟪ubi_erase_all# (vols, bflipset, vtblpnum, sqnum; wlar, q, apebs; err)⟫ ( ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum) ∧ ubi-io-inv(apebs) ∧ id(apebs, apebs0, mapped-pebs(vols)) ∧ q ⊆ q0 ∧ (err = ESUCCESS → q = []) ∧ (err = ESUCCESS ∨ ⌊err⌋ )) subst: [sqnum, vtblpnum, bflipset, vols, apebs, q, wlar, err, apebs0, q0] → [sqnum, vtblpnum3, bflipset, vols, apebs, q, wlar, err, apebs, q] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ubi-cons(apebs, vols, wlar, q, bflipset, n0, n1) ↔ # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, n1) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs, q) ∧ ¬ VTBL_VOLID ∈ vols ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, n0) ∧ valid-vtbl(apebs, vols, wlar, n0); (s)