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Proof step 30 from proof inv-create-volume (previous step)

# apebs0 = # wlar2, # apebs = # wlar, wlar2[vtblpnum].status = free, buf = mkbuf(LEB_SIZE), vtbl = to-vtbl(vols)[v, n], v ≠ VTBL_VOLID, vtblpnum < # wlar2, bflipset-cons(bflipset, wlar2), bflipset-cons(bflipset, wlar), id(apebs0, apebs, mapped-pebs(vols)), ubi-io-inv(apebs), ubi-io-inv(apebs0), unique-sqns(apebs0), unique-sqns(apebs), valid-ebatbl(apebs0, wlar2, vols, vtblpnum3), valid-ebatbl(apebs, wlar, vols, vtblpnum3), valid-eraseq(wlar2, []), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs0, vols, wlar2, vtblpnum3), valid-vtbl(apebs, vols, wlar, vtblpnum3), valid-wl(apebs0, wlar2), 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 ⊦ ⟪encode_vtbl#(; vtbl, buf; err); vols0 := vols; q0 := []; 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))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 31:
# apebs = # wlar, # apebs0 = # wlar2, wlar2[vtblpnum] = wl-entry(m, stat), buf = mkbuf(LEB_SIZE), stat = free, vtbl = to-vtbl(vols)[v, n], vtblpnum < # wlar2, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset, wlar2), id(apebs0, apebs, mapped-pebs(vols)), ubi-io-inv(apebs0), ubi-io-inv(apebs), unique-sqns(apebs), unique-sqns(apebs0), valid-ebatbl(apebs, wlar, vols, vtblpnum3), valid-ebatbl(apebs0, wlar2, vols, vtblpnum3), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-eraseq(wlar2, []), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum3), valid-vtbl(apebs0, vols, wlar2, vtblpnum3), valid-wl(apebs, wlar), valid-wl(apebs0, wlar2), 2 * ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vols + ENCODED_VOLID_SIZE ≤ LEB_SIZE ⊦ ⟪encode_vtbl#(; vtbl, buf; err); vols0 := vols; q0 := []; 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)), v = VTBL_VOLID, v ∈ vols, VTBL_VOLID ∈ vols, vtblpnum3 ∈ q

Rule argument

spec: wlentry name: elim-02 seq: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat) subst: [wle, m, stat] → [wlar2[vtblpnum], m, stat]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar2[vtblpnum], m, stat