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Proof step 23 from proof abs-istore-replay-lpt-unchanged (previous step)

# avol0 = # avol1, # lpt = # avol1, remove-refsize0(istore)[n] = indexblock(indx, lax, m), ∀ n. n < # avol1 ∧ (n ∈ nx ∨ lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n], ∀ n. (n < # avol1 ∧ replay-lpt(lpt, nx, # avol1)[n].flags = LP_INDEX_NODES ↔ n ∈ remove-refsize0(istore)) ∧ ( n ∈ remove-refsize0(istore) → abs-leb(avol0[n], remove-refsize0(istore)[n], replay-lpt(lpt, nx, # avol1)[n]) ∧ replay-lpt(lpt, nx, # avol1)[n].ref-size = remove-refsize0(istore)[n].ref-size) ⊦ (n < # avol1 ∧ replay-lpt(lpt, nx, # avol1)[n].flags = LP_INDEX_NODES ↔ n ∈ remove-refsize0(istore)) ∧ ( n ∈ remove-refsize0(istore) → abs-leb(avol1[n], indexblock(indx, lax, replay-lpt(lpt, nx, # avol1)[n].ref-size), replay-lpt(lpt, nx, # avol1)[n]) ∧ replay-lpt(lpt, nx, # avol1)[n].ref-size = m)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 24:
# lpt = # avol1, # avol0 = # avol1, remove-refsize0(istore)[n] = indexblock(indx, lax, m), replay-lpt(lpt, nx, # avol1)[n] = mklp(m0, m1, lpf, m2), ∀ n. (n < # avol1 ∧ replay-lpt(lpt, nx, # avol1)[n].flags = LP_INDEX_NODES ↔ n ∈ remove-refsize0(istore)) ∧ ( n ∈ remove-refsize0(istore) → abs-leb(avol0[n], remove-refsize0(istore)[n], replay-lpt(lpt, nx, # avol1)[n]) ∧ replay-lpt(lpt, nx, # avol1)[n].ref-size = remove-refsize0(istore)[n].ref-size), ∀ n. n < # avol1 ∧ (n ∈ nx ∨ 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, m0), replay-lpt(lpt, nx, # avol1)[n]) ∧ 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] → [replay-lpt(lpt, nx, # avol1)[n], m2, m3, lpf, m4]

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: replay-lpt(lpt, nx, # avol1)[n], m2, m3, lpf, m4