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Proof step 10 from proof abs-istore-cleanup-lpt (previous step)

# lpt = # avol1, # avol0 = # avol1, n < # avol1 ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore, remove-refsize0(istore)[n] = indexblock(indx, lax, m), lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[n] = mklp(m0, m1, lpf, m2), istore[n] = indexblock(indx0, lax0, m3), n ∈ istore → abs-leb(avol0[n], indexblock(indx0, lax0, lpt[n].ref-size), lpt[n]) ∧ lpt[n].ref-size = m3, ∀ n. n < # avol1 ∧ (lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n], ¬(n < # avol1 ∧ lpf = LP_INDEX_NODES ↔ n ∈ remove-refsize0(istore)) ∨ ¬(n ∈ remove-refsize0(istore) → abs-leb(avol1[n], indexblock(indx, lax, m), mklp(m, m1, lpf, m2)) ∧ m0 = m) ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
# avol0 = # avol1, # lpt = # avol1, n < # avol1 ∧ lpf0 = LP_INDEX_NODES ↔ n ∈ istore, istore[n] = indexblock(indx0, lax0, m3), lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[n] = mklp(m0, m1, lpf, m2), remove-refsize0(istore)[n] = indexblock(indx, lax, m), lpt[n] = mklp(m4, m5, lpf0, m6), n ∈ istore → abs-leb(avol0[n], indexblock(indx0, lax0, m4), lpt[n]) ∧ m4 = m3, ∀ n. n < # avol1 ∧ (lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n], ¬(n < # avol1 ∧ lpf = LP_INDEX_NODES ↔ n ∈ remove-refsize0(istore)) ∨ ¬(n ∈ remove-refsize0(istore) → abs-leb(avol1[n], indexblock(indx, lax, m), mklp(m, m1, lpf, m2)) ∧ m0 = m) ⊦

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] → [lpt[n], m6, m7, lpf0, m8]

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: lpt[n], m6, m7, lpf0, m8