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Proof step 19 from proof refine-wl-worker (previous step)

# apebs0 = # wlar0, # apebs = # wlar, v0 ∈ vols0 ↔ v0 ∈ avols, apebs0[n] = mkpeb(aehdr, avhdr, buf, m0, boolvar), apebs[vols0[v][m].pnum] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0), apebs0[vols0[v0][m2].pnum] = mkpeb(aehdr1, avhdr1, buf1, m3, boolvar1), abs(avols, apebs, vols0, q), bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), ebm-cons(avols), id(apebs0, apebs, mapped-pebs(vols0)), ubi-io-inv(apebs0), ubi-io-inv(apebs), unique-sqns(apebs0), unique-sqns(apebs), valid-ebatbl(apebs0, wlar0, vols0, vtblpnum0), valid-ebatbl(apebs, wlar, vols0, vtblpnum), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs0, q0), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs0, sqnum0), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs0, vols0, wlar0, vtblpnum0), valid-vtbl(apebs, vols0, wlar, vtblpnum), valid-wl(apebs0, wlar0), valid-wl(apebs, wlar), v0 ∈ vols0, q0.lebrefs ⊆ q.lebrefs ++ (VTBL_VOLID × VTBL_LNUM), v0 ∈ vols0 → # vols0[v0] = # avols[v0] ∧ (∀ m. m < # vols0[v0] → (vols0[v0][m] = unmapped → ¬ avols[v0][m].mapped?) ∧ ( vols0[v0][m] ≠ unmapped → avols[v0][m].mapped? ∧ avols[v0][m].data = apebs0[vols0[v0][m].pnum].data ∧ apebs0[vols0[v0][m].pnum].fill ≤ avols[v0][m].fill) ∧ (avols[v0][m] = erased → ¬ v0 × m ∈ q)) ⊦ VTBL_VOLID ∈ vols0, # vols0[v0] = # avols[v0] ∧ ( m2 < # vols0[v0] → (vols0[v0][m2] = unmapped → ¬ avols[v0][m2].mapped?) ∧ (vols0[v0][m2] ≠ unmapped → avols[v0][m2].mapped? ∧ avols[v0][m2].data = buf1 ∧ m3 ≤ avols[v0][m2].fill) ∧ (avols[v0][m2] = erased → ¬ v0 × m2 ∈ q0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
# vols0[v0] = # avols[v0], # apebs0 = # wlar0, # apebs = # wlar, apebs0[n] = mkpeb(aehdr, avhdr, buf, m0, boolvar), apebs[vols0[v][m].pnum] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0), apebs0[vols0[v0][m2].pnum] = mkpeb(aehdr1, avhdr1, buf1, m3, boolvar1), m2 < # avols[v0], abs(avols, apebs, vols0, q), bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), ebm-cons(avols), id(apebs0, apebs, mapped-pebs(vols0)), ubi-io-inv(apebs0), ubi-io-inv(apebs), unique-sqns(apebs0), unique-sqns(apebs), valid-ebatbl(apebs0, wlar0, vols0, vtblpnum0), valid-ebatbl(apebs, wlar, vols0, vtblpnum), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs0, q0), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs0, sqnum0), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs0, vols0, wlar0, vtblpnum0), valid-vtbl(apebs, vols0, wlar, vtblpnum), valid-wl(apebs0, wlar0), valid-wl(apebs, wlar), v0 ∈ avols, v0 ∈ vols0, q0.lebrefs ⊆ q.lebrefs ++ (VTBL_VOLID × VTBL_LNUM), ∀ m. m < # avols[v0] → (vols0[v0][m] = unmapped → ¬ avols[v0][m].mapped?) ∧ ( vols0[v0][m] ≠ unmapped → avols[v0][m].mapped? ∧ avols[v0][m].data = apebs0[vols0[v0][m].pnum].data ∧ apebs0[vols0[v0][m].pnum].fill ≤ avols[v0][m].fill) ∧ (avols[v0][m] = erased → ¬ v0 × m ∈ q) ⊦ VTBL_VOLID ∈ vols0, (vols0[v0][m2] = unmapped → ¬ avols[v0][m2].mapped?) ∧ (vols0[v0][m2] ≠ unmapped → avols[v0][m2].mapped? ∧ avols[v0][m2].data = buf1 ∧ m3 ≤ avols[v0][m2].fill) ∧ (avols[v0][m2] = erased → ¬ v0 × m2 ∈ q0)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ v ∈ avols ∧ abs(avols, apebs, vols, q) → v ∈ vols; (ss)% ⊦ v ∈ vols ∧ abs(avols, apebs, vols, q) → v ∈ avols; (ss)