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Proof step 21 from proof prepost-init-vols-sizes (previous step)

# apebs = # wlar, apebs[m0] = mkpeb(aehdr, avhdr, buf, m, boolvar), recs[VTBL_VOLID × VTBL_LNUM] = recovery-entry(m0, m1), m0 < # wlar, is-encoded(to-vtbl(vols) ∪ vtbl0, buf), unmapped-vols(vols), valid-recs(apebs, wlar, recs), valid-vtbl-weak(apebs, m0), VTBL_VOLID × VTBL_LNUM ∈ recs, v ∈ vtbl0, to-vtbl(vols) ⊥ vtbl0 ⊦ vtbl0 = ∅, v ∈ vols, ∀ v0, m. v0 ∈ vols[v, fill(mkebatbl(vtbl0[v]), unmapped)] ∧ m < # vols[v, fill(mkebatbl(vtbl0[v]), unmapped)][v0] → vols[v, fill(mkebatbl(vtbl0[v]), unmapped)][v0][m] = unmapped

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
# apebs = # wlar, apebs[m0] = mkpeb(aehdr, avhdr, buf, m, boolvar), recs[VTBL_VOLID × VTBL_LNUM] = recovery-entry(m0, m1), m0 < # wlar, m2 < # vols[v, fill(mkebatbl(vtbl0[v]), unmapped)][v0], is-encoded(to-vtbl(vols) ∪ vtbl0, buf), unmapped-vols(vols), valid-recs(apebs, wlar, recs), valid-vtbl-weak(apebs, m0), VTBL_VOLID × VTBL_LNUM ∈ recs, v ∈ vtbl0, v0 ∈ vols[v, fill(mkebatbl(vtbl0[v]), unmapped)], to-vtbl(vols) ⊥ vtbl0 ⊦ vols[v, fill(mkebatbl(vtbl0[v]), unmapped)][v0][m2] = unmapped, vtbl0 = ∅, v ∈ vols

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic