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Proof step 5 from proof abs-istore-reduce-write-idcircle (previous step)

# 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))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
# avol1 = # avol0, # lpt = # avol0, lp = mklp(m0, m1, lpf, m2), 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) → m0 = m ∧ lpf = 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))

Rule argument

spec: lprops name: elim seq: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1) subst: [lp, m, m0, lpf, m1] → [lp, m1, m2, lpf, m3]

Additional information

Used simplifier rules: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lp, m1, m2, lpf, m3