| # avol1 = # avol0, # lpt = # avol0, iblock = indexblock(indx, lax, m), id○(avol1, avol0, n), ∀ n. (n < # avol0 ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore) ∧ (n ∈ istore → abs-leb(avol0[n], istore[n], lpt[n]) ∧ lpt[n].ref-size = istore[n].ref-size) ⊦ (∀ n0. (n0 < # avol0 ∧ lpt[n, lp][n0].flags = LP_INDEX_NODES ↔ n0 ∈ istore[n, iblock]) ∧ ( n0 ∈ istore[n, iblock] → abs-leb(avol1[n0], istore[n, iblock][n0], lpt[n, lp][n0]) ∧ lpt[n, lp][n0].ref-size = istore[n, iblock][n0].ref-size)) ↔ n < # avol0 ∧ ((lpt[n].flags = LP_INDEX_NODES → lpt[n].ref-size = istore[n].ref-size) → lp.ref-size = m ∧ lp.flags = LP_INDEX_NODES) ∧ ((lpt[n].flags = LP_INDEX_NODES → abs-leb(avol0[n], istore[n], lpt[n])) → abs-leb(avol1[n], iblock, lp)) |
# lpt = # avol0, # avol1 = # avol0, id○(avol1, avol0, n), ∀ n. (n < # avol0 ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore) ∧ (n ∈ istore → abs-leb(avol0[n], istore[n], lpt[n]) ∧ lpt[n].ref-size = istore[n].ref-size) ⊦ (∀ n0. (n0 < # avol0 ∧ lpt[n, lp][n0].flags = LP_INDEX_NODES ↔ n0 ∈ istore[n, indexblock(indx, lax, m)]) ∧ ( n0 ∈ istore[n, indexblock(indx, lax, m)] → abs-leb(avol1[n0], istore[n, indexblock(indx, lax, m)][n0], lpt[n, lp][n0]) ∧ lpt[n, lp][n0].ref-size = istore[n, indexblock(indx, lax, m)][n0].ref-size)) ↔ n < # avol0 ∧ ((lpt[n].flags = LP_INDEX_NODES → lpt[n].ref-size = istore[n].ref-size) → lp.ref-size = m ∧ lp.flags = LP_INDEX_NODES) ∧ ((lpt[n].flags = LP_INDEX_NODES → abs-leb(avol0[n], istore[n], lpt[n])) → abs-leb(avol1[n], indexblock(indx, lax, m), lp))