| # apebs = # wlar, apebs[m0] = mkpeb(aehdr, avhdr, buf, m, boolvar), recs[VTBL_VOLID × VTBL_LNUM] = recovery-entry(m0, m1), vols0 = ∅, vtbl = vtbl0, recs[VTBL_VOLID × VTBL_LNUM].pnum < # apebs, m0 < # wlar, is-encoded(to-vtbl(vols) ∪ vtbl, apebs[recs[VTBL_VOLID × VTBL_LNUM].pnum].data), is-encoded(vtbl1, buf), unmapped-vols(vols), valid-recs(apebs, wlar, recs), valid-vtbl-weak(apebs, recs[VTBL_VOLID × VTBL_LNUM].pnum), valid-vtbl-weak(apebs, m0), v ∈ vols[v, mkebatbl(vtbl[v])], v ∈ vtbl, VTBL_VOLID × VTBL_LNUM ∈ recs, to-vtbl(vols) ⊥ vtbl ⊦ ⟪vtbl1 := vtbl -- v⟫ ( ( to-vtbl(vols[v, mkebatbl(vtbl[v])][v, fill(vols[v, mkebatbl(vtbl[v])][v], unmapped)]) ⊥ vtbl1 ∧ is-encoded (to-vtbl(vols[v, mkebatbl(vtbl[v])][v, fill(vols[v, mkebatbl(vtbl[v])][v], unmapped)]) ∪ vtbl1, apebs[recs[VTBL_VOLID × VTBL_LNUM].pnum].data) ∧ valid-vtbl-weak(apebs, recs[VTBL_VOLID × VTBL_LNUM].pnum) ∧ valid-recs(apebs, wlar, recs) ∧ recs[VTBL_VOLID × VTBL_LNUM].pnum < # apebs ∧ VTBL_VOLID × VTBL_LNUM ∈ recs ∧ unmapped-vols(vols[v, mkebatbl(vtbl[v])][v, fill(vols[v, mkebatbl(vtbl[v])][v], unmapped)]) ∧ # apebs = # wlar) ∧ # vtbl1 < # vtbl0), vtbl = ∅ |
# apebs = # wlar, recs[VTBL_VOLID × VTBL_LNUM] = recovery-entry(m0, m1), apebs[m0] = mkpeb(aehdr, avhdr, buf, m, boolvar), vols0 = ∅, vtbl = vtbl0, m0 < # wlar, recs[VTBL_VOLID × VTBL_LNUM].pnum < # apebs, is-encoded(vtbl1, buf), is-encoded(to-vtbl(vols) ∪ vtbl, apebs[recs[VTBL_VOLID × VTBL_LNUM].pnum].data), unmapped-vols(vols), valid-recs(apebs, wlar, recs), valid-vtbl-weak(apebs, m0), valid-vtbl-weak(apebs, recs[VTBL_VOLID × VTBL_LNUM].pnum), VTBL_VOLID × VTBL_LNUM ∈ recs, v ∈ vtbl, v ∈ vols[v, mkebatbl(vtbl[v])], to-vtbl(vols) ⊥ vtbl ⊦ vtbl = ∅, ( to-vtbl(vols[v, mkebatbl(vtbl[v])][v, fill(vols[v, mkebatbl(vtbl[v])][v], unmapped)]) ⊥ vtbl -- v ∧ is-encoded (to-vtbl(vols[v, mkebatbl(vtbl[v])][v, fill(vols[v, mkebatbl(vtbl[v])][v], unmapped)]) ∪ (vtbl -- v), apebs[recs[VTBL_VOLID × VTBL_LNUM].pnum].data) ∧ valid-vtbl-weak(apebs, recs[VTBL_VOLID × VTBL_LNUM].pnum) ∧ valid-recs(apebs, wlar, recs) ∧ recs[VTBL_VOLID × VTBL_LNUM].pnum < # apebs ∧ VTBL_VOLID × VTBL_LNUM ∈ recs ∧ unmapped-vols(vols[v, mkebatbl(vtbl[v])][v, fill(vols[v, mkebatbl(vtbl[v])][v], unmapped)]) ∧ # apebs = # wlar) ∧ #(vtbl -- v) < # vtbl0