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Proof step 11 from proof ubi-is-max-unique (previous step)

is-max(apebs, vols0, wlar0, q0, bflipset0, n0, n1), ubi-cons(apebs, vols1, wlar1, q1, bflipset1, m0, m1), # apebs = # wlar0 ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, n1) ∧ valid-wl(apebs, wlar0) ∧ valid-eraseq(q0) ∧ valid-eraseq(wlar0, q0) ∧ valid-eraseq(apebs, q0) ∧ ¬ VTBL_VOLID ∈ vols0 ∧ bflipset-cons(bflipset0, wlar0) ∧ valid-ebatbl(apebs, wlar0, vols0, n0) ∧ valid-vtbl(apebs, vols0, wlar0, n0) → vols0 ⊆ vols1, # apebs = # wlar1 ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, m1) ∧ valid-wl(apebs, wlar1) ∧ valid-eraseq(q1) ∧ valid-eraseq(wlar1, q1) ∧ valid-eraseq(apebs, q1) ∧ ¬ VTBL_VOLID ∈ vols1 ∧ bflipset-cons(bflipset1, wlar1) ∧ valid-ebatbl(apebs, wlar1, vols1, m0) ∧ valid-vtbl(apebs, vols1, wlar1, m0) → vols1 ⊆ vols0, ∃ vtbl. is-encoded(vtbl, apebs[m0].data) ∧ valid-eraseq-strong(apebs, vtbl, q1) ⊦ vols0 = vols1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
# apebs = # wlar1, bflipset-cons(bflipset1, wlar1), is-encoded(vtbl, apebs[m0].data), is-max(apebs, vols0, wlar0, q0, bflipset0, n0, n1), unique-sqns(apebs), valid-ebatbl(apebs, wlar1, vols1, m0), valid-eraseq(apebs, q1), valid-eraseq(wlar1, q1), valid-eraseq(q1), valid-eraseq-strong(apebs, vtbl, q1), valid-global-sqn(apebs, m1), valid-vtbl(apebs, vols1, wlar1, m0), valid-wl(apebs, wlar1), vols1 ⊆ vols0 ⊦ m0 ∈ q1, VTBL_VOLID ∈ vols1, vols0 ⊆ vols1, # wlar1 = # wlar0 ∧ valid-global-sqn(apebs, n1) ∧ valid-wl(apebs, wlar0) ∧ valid-eraseq(q0) ∧ valid-eraseq(wlar0, q0) ∧ valid-eraseq(apebs, q0) ∧ ¬ VTBL_VOLID ∈ vols0 ∧ bflipset-cons(bflipset0, wlar0) ∧ valid-ebatbl(apebs, wlar0, vols0, n0) ∧ valid-vtbl(apebs, vols0, wlar0, n0)

Rule argument

Additional information

Used simplifier rules: lf-vtbl-info: ⊦ valid-vtbl(apebs, vols, wlar, n) ∧ valid-eraseq(wlar, q) → ¬ n ∈ q;%vols-le-antisym: ⊦ vols0 ⊆ vols1 ∧ vols1 ⊆ vols0 → vols0 = vols1; (forward) from specification ubi-crash-recovery-base% ⊦ valid-eraseq-strong(apebs, vtbl, q) → valid-eraseq(apebs, q); (ss)% ⊦ valid-eraseq-strong(apebs, vtbl, q) → valid-eraseq(q); (ss)%⊦ 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)