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Proof step 41 from proof refine-create-volume (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
# vols[v0] = # avols[v0], # apebs0 = # wlar0, # apebs = # wlar, avols[v0][m] = erased, apebs0[unmapped.pnum] = mkpeb(aehdr, avhdr, buf, m0, boolvar), vols[v0][m] = unmapped, m < # avols[v0], abs(avols, apebs, vols, q), bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), ebm-cons(avols), id(apebs0, apebs, mapped-pebs(vols)), ubi-io-inv(apebs0), ubi-io-inv(apebs), unique-sqns(apebs0), unique-sqns(apebs), valid-ebatbl(apebs0, wlar0, vols[v, fill(mkebatbl(n), unmapped)], vtblpnum0), valid-ebatbl(apebs, wlar, vols, 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, vols[v, fill(mkebatbl(n), unmapped)], wlar0, vtblpnum0), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-wl(apebs0, wlar0), valid-wl(apebs, wlar), v0 × m ∈ q0, v0 ∈ avols, v0 ∈ vols, q0.lebrefs ⊆ ∅ ++ (VTBL_VOLID × VTBL_LNUM) ⊦ VTBL_VOLID = v, v0 × m ∈ q, VTBL_VOLID ∈ vols, v ∈ avols, v ∈ vols

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ erased.mapped?; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).fill = m; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)