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Proof step 22 from proof inv-create-volume (previous step)

# apebs = # wlar, # apebs1 = # wlar0, apebs2 = apebs1, q1 = [], wlar1 = wlar0, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset, wlar0), id(apebs1, apebs, mapped-pebs(vols)), ubi-io-inv(apebs1), ubi-io-inv(apebs), unique-sqns(apebs), unique-sqns(apebs1), valid-ebatbl(apebs, wlar, vols, vtblpnum3), valid-ebatbl(apebs1, wlar0, vols, vtblpnum3), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-eraseq(wlar0, []), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs1, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum3), valid-vtbl(apebs1, vols, wlar0, vtblpnum3), valid-wl(apebs, wlar), valid-wl(apebs1, wlar0), 2 * ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vols + ENCODED_VOLID_SIZE ≤ LEB_SIZE ⊦ ∀ vtblpnum, wlar0, q1, apebs1, err. (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err ≠ ESUCCESS → # apebs1 = # wlar0 ∧ unique-sqns(apebs1) ∧ valid-global-sqn(apebs1, sqnum) ∧ valid-wl(apebs1, wlar0) ∧ valid-eraseq(q1) ∧ valid-eraseq(wlar0, q1) ∧ valid-eraseq(apebs1, q1) ∧ bflipset-cons(bflipset, wlar0) ∧ valid-ebatbl(apebs1, wlar0, vols, vtblpnum3) ∧ valid-vtbl(apebs1, vols, wlar0, vtblpnum3)) ∧ ubi-io-inv(apebs1) ∧ q1.lebrefs = ∅ ∧ id(apebs1, apebs2, mapped-pebs(vols)) ∧ ( err = ESUCCESS → vtblpnum < # apebs1 ∧ wlar0[vtblpnum].status = free ∧ apebs2 = apebs1 ∧ wlar1 = wlar0 ∧ [] = q1 ∧ # apebs1 = # wlar0 ∧ unique-sqns(apebs1) ∧ valid-global-sqn(apebs1, sqnum) ∧ valid-wl(apebs1, wlar0) ∧ valid-eraseq(wlar0, []) ∧ bflipset-cons(bflipset, wlar0) ∧ valid-ebatbl(apebs1, wlar0, vols, vtblpnum3) ∧ valid-vtbl(apebs1, vols, wlar0, vtblpnum3)) → ⟪vols0 := vols; 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, wlar0, q1, bflipset, vtblpnum3, sqnum, apebs1; err); if err = ESUCCESS then {vols[v] := mkebatbl(n); vols[v] := fill(vols[v], unmapped)}}}}⟫ ( # apebs1 = # wlar0 ∧ unique-sqns(apebs1) ∧ valid-global-sqn(apebs1, sqnum) ∧ valid-wl(apebs1, wlar0) ∧ valid-eraseq(q1) ∧ valid-eraseq(wlar0, q1) ∧ valid-eraseq(apebs1, q1) ∧ ¬ VTBL_VOLID ∈ vols ∧ bflipset-cons(bflipset, wlar0) ∧ valid-ebatbl(apebs1, wlar0, vols, vtblpnum3) ∧ valid-vtbl(apebs1, vols, wlar0, vtblpnum3) ∧ ubi-io-inv(apebs1) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id(apebs1, apebs, mapped-pebs(vols)) ∧ (err = ESUCCESS → ¬ v ∈ vols0 ∧ vols = vols0[v, fill(mkebatbl(n), unmapped)] ∧ q1.lebrefs ⊆ ∅ ++ (VTBL_VOLID × VTBL_LNUM)) ∧ (err ≠ ESUCCESS → q1.lebrefs ⊆ q.lebrefs ∧ vols = vols0)), v = VTBL_VOLID, v ∈ vols, VTBL_VOLID ∈ vols, vtblpnum3 ∈ q

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
# apebs = # wlar, # apebs1 = # wlar0, q0.lebrefs = ∅, v ≠ VTBL_VOLID, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset, wlar0), id(apebs1, apebs, mapped-pebs(vols)), id(apebs0, apebs1, mapped-pebs(vols)), id(apebs0, apebs, mapped-pebs(vols)), ubi-io-inv(apebs1), ubi-io-inv(apebs), ubi-io-inv(apebs0), unique-sqns(apebs), unique-sqns(apebs1), valid-ebatbl(apebs, wlar, vols, vtblpnum3), valid-ebatbl(apebs1, wlar0, vols, vtblpnum3), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-eraseq(wlar0, []), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs1, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum3), valid-vtbl(apebs1, vols, wlar0, vtblpnum3), valid-wl(apebs, wlar), valid-wl(apebs1, wlar0), 2 * ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vols + ENCODED_VOLID_SIZE ≤ LEB_SIZE, ¬ v ∈ vols, ¬ VTBL_VOLID ∈ vols, ¬ vtblpnum3 ∈ q, err = ESUCCESS → vtblpnum < # apebs0 ∧ wlar2[vtblpnum].status = free ∧ apebs1 = apebs0 ∧ wlar0 = wlar2 ∧ [] = q0, err ≠ ESUCCESS → # apebs0 = # wlar2 ∧ unique-sqns(apebs0) ∧ valid-global-sqn(apebs0, sqnum) ∧ valid-wl(apebs0, wlar2) ∧ valid-eraseq(q0) ∧ valid-eraseq(wlar2, q0) ∧ valid-eraseq(apebs0, q0) ∧ bflipset-cons(bflipset, wlar2) ∧ valid-ebatbl(apebs0, wlar2, vols, vtblpnum3) ∧ valid-vtbl(apebs0, vols, wlar2, vtblpnum3), err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟪vols0 := vols; 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, wlar2, q0, bflipset, vtblpnum3, sqnum, apebs0; err); if err = ESUCCESS then {vols[v] := mkebatbl(n); vols[v] := fill(vols[v], unmapped)}}}}⟫ ( # apebs0 = # wlar2 ∧ unique-sqns(apebs0) ∧ valid-global-sqn(apebs0, sqnum) ∧ valid-wl(apebs0, wlar2) ∧ valid-eraseq(q0) ∧ valid-eraseq(wlar2, q0) ∧ valid-eraseq(apebs0, q0) ∧ ¬ VTBL_VOLID ∈ vols ∧ bflipset-cons(bflipset, wlar2) ∧ valid-ebatbl(apebs0, wlar2, vols, vtblpnum3) ∧ valid-vtbl(apebs0, vols, wlar2, vtblpnum3) ∧ ubi-io-inv(apebs0) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id(apebs0, apebs, mapped-pebs(vols)) ∧ (err = ESUCCESS → ¬ v ∈ vols0 ∧ vols = vols0[v, fill(mkebatbl(n), unmapped)] ∧ q0.lebrefs ⊆ ∅ ++ (VTBL_VOLID × VTBL_LNUM)) ∧ (err ≠ ESUCCESS → q0.lebrefs ⊆ q.lebrefs ∧ vols = vols0))

Rule argument

Additional information

Used simplifier rules: int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]% ⊦ ns ∩ ns = ns; (s)%idset-trans-intersect: ⊦ id(apebs2, apebs1, ns0) ∧ id(apebs1, apebs0, ns1) → id(apebs2, apebs0, ns0 ∩ ns1); (forward) from specification ubi-base