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Proof step 11 from proof inv-erase (previous step)

# wlar = # wlar0, # apebs = # wlar0, vtblpnum0 < # vols[v], bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, vtblpnum), valid-ebatbl(apebs, wlar, vols, vtblpnum), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs, q0), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols0, wlar0, vtblpnum), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-wl(apebs, wlar0), valid-wl(apebs, wlar), v ∈ vols, ¬ vtblpnum ∈ q, ¬ VTBL_VOLID ∈ vols, ¬ VTBL_VOLID ∈ vols0, ¬ vtblpnum ∈ q0 ⊦ ⟪ubi_erase_all#(vols0, bflipset0, vtblpnum, sqnum; wlar0, q0, apebs; err)⟫ ( # apebs = # wlar0 ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ valid-wl(apebs, wlar0) ∧ valid-eraseq(q0) ∧ valid-eraseq(wlar0, q0) ∧ valid-eraseq(apebs, q0) ∧ bflipset-cons(bflipset0, wlar0) ∧ valid-ebatbl(apebs, wlar0, vols0, vtblpnum) ∧ valid-vtbl(apebs, vols0, wlar0, vtblpnum) ∧ ubi-io-inv(apebs))

User applied rule insert program lemma

And obtained the following new goals

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, vtblpnum, bflipset0, vols0, apebs, q0, wlar0, err, apebs, q0] 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)